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------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/master06.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAAD4AAAAAYALgAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwCeQChAAMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAOAAAAJAMFAP///////3gA oAB4AKAA////////CAAAAPoCAAAAAAAAAAAAAAQAAAAtAQIABwAAAPwCAAD///8AAAAEAAAALQED AAQAAAAnAf//HAAAAPsC9v8AAAAAAACQAQAAAAAAQAAAQXJpYWwAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAEAAAALQEEAAQAAAAuARgABAAAAAIBAQAFAAAACQIAAAACLgAAADIKEgAXABoAAABT b2x2aW5nIFJhdGlvbmFsIEVxdWF0aW9ucwcABQADAAQAAwAFAAYAAwAGAAYAAgADAAUABgAFAAIA AwAGAAYABQAGAAIAAwAFAAYABAAEAAAALgEAABwAAAD7AhAABwAAAAAAvAIAAAAAAQICIlN5c3Rl bQAAAAAAAAAAAAAYAAAAAgAAAJg6FQDkBAAABAAAAC0BBQAEAAAA8AEEAAMAAAAAAA== ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0001.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0002.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in a way without using fractions.
------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0003.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in a way without using fractions.
Example: Suppose the value of 2/3 of an apple is
the same as the value of ¾ of an orange, restate
this relation in whole values.
------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0004.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in a way without using fractions.
Example: Suppose the value of 2/3 of an apple is
the same as the value of ¾ of an orange, restate
this relation in whole values.
To restat= e a rational
equation:=
------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0005.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in a way without using fractions.
Example: Suppose the value of 2/3 of an apple is
the same as the value of ¾ of an orange, restate
this relation in whole values.
To restat= e a rational
equation:=
= I.Find the LCD
------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0006.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in a way without using fractions.
Example: Suppose the value of 2/3 of an apple is
the same as the value of ¾ of an orange, restate
this relation in whole values.
To restat= e a rational
equation:=
= I.Find the LCD
= II.Multiply the LCD <= /span>
to the eq= uation, distribute
It to eac= h term to clear
every denominator.
------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0007.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in a way without using fractions.
Example: Suppose the value of 2/3 of an apple is
the same as the value of ¾ of an orange, restate
this relation in whole values.
        = ;            &n= bsp;  
To restat= e a rational
equation:=
= I.Find the LCD
= II.Multiply the LCD <= /span>
to the eq= uation, distribute
It to eac= h term to clear
every denominator.
------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0007_image001.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjBoYHvAzMgJYhVEMzIAGcymjECCQQYsywrEnEwwFhMjI5TFyPT//38w S49RAirGDVfHw/SAuYFNCMhSY+NnkGL4D1LMIADkHwCydgCxAxsDwwxmoB6oGh4G38SSjJDKglSg GgYOoOgvJogOEGABYl1GiNkiTAxMDmCWMJClwQgT+8QME7vFAnL7b6aGfxDdE8CuZmFiEAjJzE0t VvBLLVcIys9NzGO4Mf9z+UMgVlD4Wu4jmLYcYg8j2H4jrgQmAVaQTvdKGL8DbJJjJbr5DCSZzwT2 zwe4PT3MPCwgI0yg9uQxQvjGlTD5KAZkfh4jhG+EzR1MIHcEV+Ym5ecwMKwR4sr58lEIpz8h7mCC +/cAE8gI20ouaKxwgWMO7D0GiF0CDOxg3h5wXDMyMSkFVxaXpOYyLAeZywDUocjQBdYAUiDwRYgB 3c/MYP0A4QeM7oACAAA= ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0007_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhggAoAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAYABQBs ACAAhAAAAAAAAA0IBQAFCAsLDQ0ICAUAAAAFCwUFCw0LCwUFCAUIDQsICwsIBQ0ICwsFAAUICwgF BQsFBQgIDQgFAAAABQgICwsLCwgFCAUABQECAwECAwECAwECAwECAwECAwX/ICAKQTAQYqqubOu+ cJwWRnDI+FogQGLcuaBwqEooCL4FMcZAARqnpXTKcjgfSipMANR6p9zvCysuCx82s46nbsdoEHci 4nTbW9B6WTK5+1lhag1ZAll/dgkUhmJoJQEVeodiJCWLkkQJFpdqNCUDFxiRX4lxm6MUFX0ANF1m DQGWpkuJUSmDbQUQirJaDak6qmVGFxnBvJgUrXcSBAUZojCJjo7Kdz6lAJSPBNPd3o4vryWQpt/m 4EUG2D0/ZrkjtTnS3dWIFPECv2IFRyJ5x1NYpXgQj4q0VPPIAZxVw1GshRAjSsRVo97EIIkeGjyS 5KKUVxqnWBFBxuOQXLvcMwQyiRHDhZRq0Fhk6YJPRjtwaOIo1ANmm386YTRytM7MyqAxbsrxifSF 0jLaQjYtwpRKCAA7 ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0008.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in a way without using fractions.
Example: Suppose the value of 2/3 of an apple is
the same as the value of ¾ of an orange, restate
this relation in whole values.
        = ;            &n= bsp;   LCD =3D12         = ;            &n= bsp;              = ;            &n= bsp;            = ;            &n= bsp;           
To restat= e a rational
equation:=
= I.Find the LCD
= II.Multiply the LCD <= /span>
to the eq= uation, distribute
It to eac= h term to clear
every denominator.
------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0008_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhggAoAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAYABQBs ACAAhAAAAAAAAA0IBQAFCAsLDQ0ICAUAAAAFCwUFCw0LCwUFCAUIDQsICwsIBQ0ICwsFAAUICwgF BQsFBQgIDQgFAAAABQgICwsLCwgFCAUABQECAwECAwECAwECAwECAwECAwX/ICAKQTAQYqqubOu+ cJwWRnDI+FogQGLcuaBwqEooCL4FMcZAARqnpXTKcjgfSipMANR6p9zvCysuCx82s46nbsdoEHci 4nTbW9B6WTK5+1lhag1ZAll/dgkUhmJoJQEVeodiJCWLkkQJFpdqNCUDFxiRX4lxm6MUFX0ANF1m DQGWpkuJUSmDbQUQirJaDak6qmVGFxnBvJgUrXcSBAUZojCJjo7Kdz6lAJSPBNPd3o4vryWQpt/m 4EUG2D0/ZrkjtTnS3dWIFPECv2IFRyJ5x1NYpXgQj4q0VPPIAZxVw1GshRAjSsRVo97EIIkeGjyS 5KKUVxqnWBFBxuOQXLvcMwQyiRHDhZRq0Fhk6YJPRjtwaOIo1ANmm386YTRytM7MyqAxbsrxifSF 0jLaQjYtwpRKCAA7 ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0009.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in a way without using fractions.
Example: Suppose the value of 2/3 of an apple is
the same as the value of ¾ of an orange, restate
this relation in whole values.
        = ;            &n= bsp;   LCD =3D12         = ;            &n= bsp;              = ;            &n= bsp;            = ;            &n= bsp;           
(        = ;           ) *12
To restat= e a rational
equation:=
= I.Find the LCD
= II.Multiply the LCD <= /span>
to the eq= uation, distribute
It to eac= h term to clear
every denominator.
------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0009_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhggAoAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAYABQBs ACAAhAAAAAAAAA0IBQAFCAsLDQ0ICAUAAAAFCwUFCw0LCwUFCAUIDQsICwsIBQ0ICwsFAAUICwgF BQsFBQgIDQgFAAAABQgICwsLCwgFCAUABQECAwECAwECAwECAwECAwECAwX/ICAKQTAQYqqubOu+ cJwWRnDI+FogQGLcuaBwqEooCL4FMcZAARqnpXTKcjgfSipMANR6p9zvCysuCx82s46nbsdoEHci 4nTbW9B6WTK5+1lhag1ZAll/dgkUhmJoJQEVeodiJCWLkkQJFpdqNCUDFxiRX4lxm6MUFX0ANF1m DQGWpkuJUSmDbQUQirJaDak6qmVGFxnBvJgUrXcSBAUZojCJjo7Kdz6lAJSPBNPd3o4vryWQpt/m 4EUG2D0/ZrkjtTnS3dWIFPECv2IFRyJ5x1NYpXgQj4q0VPPIAZxVw1GshRAjSsRVo97EIIkeGjyS 5KKUVxqnWBFBxuOQXLvcMwQyiRHDhZRq0Fhk6YJPRjtwaOIo1ANmm386YTRytM7MyqAxbsrxifSF 0jLaQjYtwpRKCAA7 ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0009_image005.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjBoYHvAzMgJYhVEMzIAGcymjECCQQYsywrEnEwwFhMjI5TFyPT//38w S49RAirGDVfHw/SAuYFNCMhSY+NnkGL4D1LMIADkHwCydgCxAxsDwwxmoB6oGh4G38SSjJDKglSg GgYOoOgvJogOEGABYl1GiNkiTAxMDmCWMJClwQgT+8QME7vFAnL7b6aGfxDdE8CuZmFiEAjJzE0t VvBLLVcIys9NzGO4Mf9z+UMgVlD4Wl4vknYKYg8j2H4jrgQmAVaQTvdKGL8DbJJjJbr5DCSZzwT2 zwe4PT3MPCwgI0yg9uQxQvjGlTD5KAZkfh4jhG+EzR1MIHcEV+Ym5ecwMGwR46o98UQIpz8h7mCC +/cAE8gI20ouaKxwgWMO7D0GiF0CDOxg3h5wXDMyMSkFVxaXpOYynAKZywDUocjQBdYAUvDkmRAD up+ZwfoBBo3uqIACAAA= ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0009_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhggAnAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAYABQBs AB8AhAAAAAAAAA0IBQAFCAsLDQ0ICAUAAAAFCwUFCw0LCwUFCAUIDQsICwsIBQ0ICwsFAAUICwgF BQsFBQgIDQgFAAAABQgICwsLCwgFCAUABQECAwECAwECAwECAwECAwECAwX/ICAKQTAQYqqubOu+ cJwWRnDI+FogQGLcuaBwqEooCL4FMcZAARqnpXTKcjgfSipMANR6p9zvCysuCx82s46nbsdoEHci 4nTbW9B6WTK5+1lhag1ZAll/dgkUhmJoJQEVekQJFoeAjotCNCUDFxiRX4lxlWWJFX0ANF1mDQGY o1OJUSmDbQUQiq9fDaY6p6QKFxm+uVKJqncSBAUZnzCJjo7Hdz6iACQlkGWs2M3EQdRFPyLQ5OWO LrYjsjnP5NIv5vHnRRTrArxiBUcied5UqSkerKPyzFS7bP6K1biUsKHDh7k0vYMoJJErLUaQGLhI MQcrjlOsiCDTkYgtXG4CMpWsiOECSjVoJq58wceiHTgzcxTq8bJNv5wxGjmqpkYlUBk25fQ86myp l2utmLJzOiUEADs= ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0009_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhsQBbAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQCs AFkAgQAAAAAAAP8zAAECAwL/hI+py+0PIxNU2ouz3ryrWnniSJamFZ7qyrYRBbuyKswrnNo6V+90 7wtegEJRrIj8AInJTa6ZDD2hienBSo0ESlJm9mrFfhmB8naUEo+Va63ZlMZ523TL+ySX1/eXu6dc lcc3KOH3d4awRLjoAFiCOMEoiWBoMze5V2mJuaipc8n55fkZWje6A1padOqTqurj+CprEjtre3ib 21Gr21sI6Rv8ACxcbHyMnKy8PMnKSMx84EzIG20wTQ2duVLNiZ313afd3J05vhFuft5WztFOvr72 rjH/XC8PHN+o38kvCu0vwb1+mDwFlJZr4D9tBwE0VJfhIYl2ByWaqmgGkMWI/+cCbmSHMWM6d+8U +vInUuBHN+tM6lKYEta0lao8iqTJ0o01dDddYshYiFvPMziF3AGqAqnOpENHjjGkVERUCD5z1nK6 UCVWSlOpsohV9SLAm+K6Ui2qUhraJvOaujW7VCjXWzDfwv3VolLYneJc6F3LN61fgIG/AlbQbW9h MocRj138qLFjxpClSu5bmefln5npbebYGTO+0Dkvkt43SPGyrTJPC7bn2qHqILNP1jb6WRJrKrvp 9uadW13wGbcL/gbJ7O6s4nyOZyum3LZt5rqpr3Je07qOmJWxE4/O17tQ8cHIWzZvDH1Z9cnA0yIb 2zP6ofEnwudIv75hu/yH6wbX6pZrBQAAOw== ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0010.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in a way without using fractions.
Example: Suppose the value of 2/3 of an apple is
the same as the value of ¾ of an orange, restate
this relation in whole values.
        = ;            &n= bsp;   LCD =3D12         = ;            &n= bsp;              = ;            &n= bsp;            = ;            &n= bsp;           
(        = ;           ) *12
To restat= e a rational
equation:=
= I.Find the LCD
= II.Multiply the LCD <= /span>
to the eq= uation, distribute
It to eac= h term to clear
every denominator.
------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0010_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhggAoAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAYABQBs ACAAhAAAAAAAAA0IBQAFCAsLDQ0ICAUAAAAFCwUFCw0LCwUFCAUIDQsICwsIBQ0ICwsFAAUICwgF BQsFBQgIDQgFAAAABQgICwsLCwgFCAUABQECAwECAwECAwECAwECAwECAwX/ICAKQTAQYqqubOu+ cJwWRnDI+FogQGLcuaBwqEooCL4FMcZAARqnpXTKcjgfSipMANR6p9zvCysuCx82s46nbsdoEHci 4nTbW9B6WTK5+1lhag1ZAll/dgkUhmJoJQEVeodiJCWLkkQJFpdqNCUDFxiRX4lxm6MUFX0ANF1m DQGWpkuJUSmDbQUQirJaDak6qmVGFxnBvJgUrXcSBAUZojCJjo7Kdz6lAJSPBNPd3o4vryWQpt/m 4EUG2D0/ZrkjtTnS3dWIFPECv2IFRyJ5x1NYpXgQj4q0VPPIAZxVw1GshRAjSsRVo97EIIkeGjyS 5KKUVxqnWBFBxuOQXLvcMwQyiRHDhZRq0Fhk6YJPRjtwaOIo1ANmm386YTRytM7MyqAxbsrxifSF 0jLaQjYtwpRKCAA7 ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0010_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhggAnAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAYABQBs AB8AhAAAAAAAAA0IBQAFCAsLDQ0ICAUAAAAFCwUFCw0LCwUFCAUIDQsICwsIBQ0ICwsFAAUICwgF BQsFBQgIDQgFAAAABQgICwsLCwgFCAUABQECAwECAwECAwECAwECAwECAwX/ICAKQTAQYqqubOu+ cJwWRnDI+FogQGLcuaBwqEooCL4FMcZAARqnpXTKcjgfSipMANR6p9zvCysuCx82s46nbsdoEHci 4nTbW9B6WTK5+1lhag1ZAll/dgkUhmJoJQEVekQJFoeAjotCNCUDFxiRX4lxlWWJFX0ANF1mDQGY o1OJUSmDbQUQiq9fDaY6p6QKFxm+uVKJqncSBAUZnzCJjo7Hdz6iACQlkGWs2M3EQdRFPyLQ5OWO LrYjsjnP5NIv5vHnRRTrArxiBUcied5UqSkerKPyzFS7bP6K1biUsKHDh7k0vYMoJJErLUaQGLhI MQcrjlOsiCDTkYgtXG4CMpWsiOECSjVoJq58wceiHTgzcxTq8bJNv5wxGjmqpkYlUBk25fQ86myp l2utmLJzOiUEADs= ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0010_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAT AAoAgAAAAAAAAAIWhI9pEerbnmJyxnooznfrDXxe54FJAQA7 ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0010_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIQAzAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAg ADEAgAAAAAAAAAJThI+paxEMY5NUuYpnxm/T60ldCIEkM55LqiJm68IWK9O1nLy43eo3HgM2eCpi UYhMKoHGo7J5gpKkIarHusFmtJwlt/L9eMdPcjIsMiPREXYpVAAAOw== ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0010_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhSgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABI AAEAgAAAAAAAAAIHjI+py+2vCgA7 ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0010_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCgAQAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAMAAgAF AA0AgAAAAAAAAAIPBGKGGtv44lPp1EUTttoUADs= ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0013.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in a way without using fractions.
Example: Suppose the value of 2/3 of an apple is
the same as the value of ¾ of an orange, restate
this relation in whole values.
        = ;            &n= bsp;   LCD =3D12         = ;            &n= bsp;              = ;            &n= bsp;            = ;            &n= bsp;           
(        = ;           ) *12
To restat= e a rational
equation:=
= I.Find the LCD
= II.Multiply the LCD <= /span>
to the eq= uation, distribute
It to eac= h term to clear
every denominator.
3
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Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in a way without using fractions.
Example: Suppose the value of 2/3 of an apple is
the same as the value of ¾ of an orange, restate
this relation in whole values.
        = ;            &n= bsp;   LCD =3D12         = ;            &n= bsp;              = ;            &n= bsp;            = ;            &n= bsp;           
(        = ;           ) *12
To restat= e a rational
equation:=
= I.Find the LCD
= II.Multiply the LCD <= /span>
to the eq= uation, distribute
It to eac= h term to clear
every denominator.
3
------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0011_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhggAoAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAYABQBs ACAAhAAAAAAAAA0IBQAFCAsLDQ0ICAUAAAAFCwUFCw0LCwUFCAUIDQsICwsIBQ0ICwsFAAUICwgF BQsFBQgIDQgFAAAABQgICwsLCwgFCAUABQECAwECAwECAwECAwECAwECAwX/ICAKQTAQYqqubOu+ cJwWRnDI+FogQGLcuaBwqEooCL4FMcZAARqnpXTKcjgfSipMANR6p9zvCysuCx82s46nbsdoEHci 4nTbW9B6WTK5+1lhag1ZAll/dgkUhmJoJQEVeodiJCWLkkQJFpdqNCUDFxiRX4lxm6MUFX0ANF1m DQGWpkuJUSmDbQUQirJaDak6qmVGFxnBvJgUrXcSBAUZojCJjo7Kdz6lAJSPBNPd3o4vryWQpt/m 4EUG2D0/ZrkjtTnS3dWIFPECv2IFRyJ5x1NYpXgQj4q0VPPIAZxVw1GshRAjSsRVo97EIIkeGjyS 5KKUVxqnWBFBxuOQXLvcMwQyiRHDhZRq0Fhk6YJPRjtwaOIo1ANmm386YTRytM7MyqAxbsrxifSF 0jLaQjYtwpRKCAA7 ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0011_image021.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhggAnAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAYABQBs AB8AhAAAAAAAAA0IBQAFCAsLDQ0ICAUAAAAFCwUFCw0LCwUFCAUIDQsICwsIBQ0ICwsFAAUICwgF BQsFBQgIDQgFAAAABQgICwsLCwgFCAUABQECAwECAwECAwECAwECAwECAwX/ICAKQTAQYqqubOu+ cJwWRnDI+FogQGLcuaBwqEooCL4FMcZAARqnpXTKcjgfSipMANR6p9zvCysuCx82s46nbsdoEHci 4nTbW9B6WTK5+1lhag1ZAll/dgkUhmJoJQEVekQJFoeAjotCNCUDFxiRX4lxlWWJFX0ANF1mDQGY o1OJUSmDbQUQiq9fDaY6p6QKFxm+uVKJqncSBAUZnzCJjo7Hdz6iACQlkGWs2M3EQdRFPyLQ5OWO LrYjsjnP5NIv5vHnRRTrArxiBUcied5UqSkerKPyzFS7bP6K1biUsKHDh7k0vYMoJJErLUaQGLhI MQcrjlOsiCDTkYgtXG4CMpWsiOECSjVoJq58wceiHTgzcxTq8bJNv5wxGjmqpkYlUBk25fQ86myp l2utmLJzOiUEADs= ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0011_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEwALAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAT AAoAgAAAAAAAAAIWhI9pEerbnmJyxnooznfrDXxe54FJAQA7 ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0011_image023.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIQAzAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAg ADEAgAAAAAAAAAJThI+paxEMY5NUuYpnxm/T60ldCIEkM55LqiJm68IWK9O1nLy43eo3HgM2eCpi UYhMKoHGo7J5gpKkIarHusFmtJwlt/L9eMdPcjIsMiPREXYpVAAAOw== ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0011_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhlQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACT AAEAgAAAAAAAAAIKjI+py+0Po5z0FQA7 ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0011_image025.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAAYAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAN ABYAgAAAAAAAAAIjhI8WmbF8HgRuKksl1KxajlFhhjkgYp6ZOaXeNqpoTIdyNBUAOx== ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0011_image026.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDAANAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAK AAwAgAAAAAAAAAIXhB8Hkdb+3oqszpqwRWwq1X2Q6JClKRUAOx== ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0064.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
An equati= on or relation expressed using fractions may always be restated in a way without using fractions.
Example: Suppose the value of 2/3 of an apple is
the same as the value of ¾ of an orange, restate
this relation in whole values.
        = ;            &n= bsp;   LCD =3D12         = ;            &n= bsp;              = ;            &n= bsp;            = ;            &n= bsp;           
(        = ;           ) *12
To restat= e a rational
equation:=
= I.Find the LCD
= II.Multiply the LCD <= /span>
to the eq= uation, distribute
It to eac= h term to clear
every denominator.
3
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Solving Rational Equations
Example: Suppose the value of 3/4 of an apple
and 5/3 of a coconut the same as the value of 5/6 of = a watermelon. Restate this relation in whole values.<= /div>
To restat= e a rational
equation:=
= I.Find the LCD
= II.Multiply the LCD <= /span>
to the eq= uation, distribute
It to eac= h term to clear
every denominator.
------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0012.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
Example: Suppose the value of 3/4 of an apple
and 3/5 of a coconut the same as the value of 5/6 of = a watermelon. Restate this relation in whole values.
        = ;            &n= bsp;       
To restat= e a rational
equation:=
= I.Find the LCD
= II.Multiply the LCD <= /span>
to the eq= uation, distribute
It to eac= h term to clear
every denominator.
------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0012_image036.wmz Content-Transfer-Encoding: base64 Content-Type: image/x-wmz H4sIAAAAAAACC7t+9tgsBjBo4HzAzMAJYhWGMIIYzPGMQIJBBizLCsScTDAWEyMjlMXI9P//fzBL j1ECKsYNV8fD9IC5gVMIyFJj42eQYvgPUswgAOQfALJ2ALED0KIZzEA9UDU8DL6JJRkhlQWpQDUM HEDRX0wQHSDAAsS6jBCzRZgYmBzALGEgS4IJJtbGDBPLYoWJMbHDxEw4Qf75zdTwD2LiBEawuUwM AiGZuanFCn6p5QpB+bmJeQw35n8ufwjECgpfy4X5035D7GYEu8mIq4d5HztIq1klhJ/HKADmm1bC 5KVZkPl5jFOYQXxjuPwlBhDfBC7vxwCRR3cfI0nuYwKH0Qe4O/MY14DdFQ63xwnsLmc4Xw1sg2Ml lnBhAtkbXJmblJ/DwFAnyvX1xBMhnOECsZcJam8C0wVWkBG2lTB+GhOIr13JBY1pLnBqAAc/A8Ru AQZ2MG8POP0wMjEpBVcWl6TmMvwG2cMA1KHI0AXWAFLw5JkQA7qfmcH6AY4WykDUAgAA ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0012_image037.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhwQAvAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAYABgC1 ACUAhAAAAAAAAAsIBQAABQsLDQ0IBQUIDQ0LCwUAAAgIDQsFAAUICwUFBQAFCw0ICAUABQgFAAAF CAgICwUFCAUFCwgIBQgICAsICwgFBQsFBQgFCAUFAAECAwECAwECAwECAwX/ICAKQTAQYqquamGw cCzPAGmi9IGUQ+LSwCBNUQosVroio2i0BV5CQOGoa0RFjkfiyoVNAdXZAfIUjXvdtMyxM22RkAhq bBUp5NeDJCU4Rc9valx6fH4wOoZYEziCjQAKUDF0IgUBdQ6LjQpHUQoMiY5dmzIKaCoHFKGNSZyH CFQVr2APjGkKdUIFDQJ4qly3MpW4vqpOpkiyAhYILwKRXZVuQpgEd7XEM9HHK6WB2I4XYDugWMx6 bAbUjmzbkhgJk9/TCO1gEOTyjiTPlE8ZBAUGSHinqhI/GESKDMuXrQyyXgxDjWmVIqCFLX0qUFzF jIYuM7Ii5ugIB59IWwf7/2QiAdHRAS0z1AFAd1IMTBYkNqKq+QfDtUemujViw2lUsEQGeaYgamdj ijFGKppUCsannYOPWhkVlKQE1nIl5HQN0FLk2K98mCykeoqM10NWwWj4ybau3bt48+rdy1fel76A A2P7K7iwYWhOD9thwiSx4ruEH0t+nJCxpcmYY1jezLnzZo+ONXseTZoJKc6hV5RezboE38iZYwuG Lbv2Xtq2c+vezbu3b2y86BqunBoz1KnY2JQ9zIaHN9vClB7AsGH5cLSy+zwXKWBBHOGBWfWmqdQB hTHWBRvbHvuOjfS+phNADx5wuCTIH4uPHtGZPfiG7ZMbeUCxp4oDnNAn2zZEA5IkRT2+VMYEdoVB 0mAkARmIjYKxyZdbPFIAGN93knn4CIWPMaUDiqpwqBhUb/HWnENqhAAAOw== ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0015.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
Example: Suppose the value of 3/4 of an apple
and 3/5 of a coconut the same as the value of 5/6 of = a watermelon. Restate this relation in whole values.
        = ;            &n= bsp;       
LCD =3D60
To restat= e a rational
equation:=
= I.Find the LCD
= II.Multiply the LCD <= /span>
to the eq= uation, distribute
It to eac= h term to clear
every denominator.
------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0015_image038.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhwQAvAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAYABgC1 ACUAhAAAAAAAAAsIBQAABQsLDQ0IBQUIDQ0LCwUAAAgIDQsFAAUICwUFBQAFCw0ICAUABQgFAAAF CAgICwUFCAUFCwgIBQgICAsICwgFBQsFBQgFCAUFAAECAwECAwECAwECAwX/ICAKQTAQYqquamGw cCzPAGmi9IGUQ+LSwCBNUQosVroio2i0BV5CQOGoa0RFjkfiyoVNAdXZAfIUjXvdtMyxM22RkAhq bBUp5NeDJCU4Rc9valx6fH4wOoZYEziCjQAKUDF0IgUBdQ6LjQpHUQoMiY5dmzIKaCoHFKGNSZyH CFQVr2APjGkKdUIFDQJ4qly3MpW4vqpOpkiyAhYILwKRXZVuQpgEd7XEM9HHK6WB2I4XYDugWMx6 bAbUjmzbkhgJk9/TCO1gEOTyjiTPlE8ZBAUGSHinqhI/GESKDMuXrQyyXgxDjWmVIqCFLX0qUFzF jIYuM7Ii5ugIB59IWwf7/2QiAdHRAS0z1AFAd1IMTBYkNqKq+QfDtUemujViw2lUsEQGeaYgamdj ijFGKppUCsannYOPWhkVlKQE1nIl5HQN0FLk2K98mCykeoqM10NWwWj4ybau3bt48+rdy1fel76A A2P7K7iwYWhOD9thwiSx4ruEH0t+nJCxpcmYY1jezLnzZo+ONXseTZoJKc6hV5RezboE38iZYwuG Lbv2Xtq2c+vezbu3b2y86BqunBoz1KnY2JQ9zIaHN9vClB7AsGH5cLSy+zwXKWBBHOGBWfWmqdQB hTHWBRvbHvuOjfS+phNADx5wuCTIH4uPHtGZPfiG7ZMbeUCxp4oDnNAn2zZEA5IkRT2+VMYEdoVB 0mAkARmIjYKxyZdbPFIAGN93knn4CIWPMaUDiqpwqBhUb/HWnENqhAAAOw== ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0016.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
Example: Suppose the value of 3/4 of an apple
and 3/5 of a coconut the same as the value of 5/6 of = a watermelon. Restate this relation in whole values.
        = ;            &n= bsp;       
LCD =3D60
(        = ;            &n= bsp;       ) *60
To restat= e a rational
equation:=
= I.Find the LCD
= II.Multiply the LCD <= /span>
to the eq= uation, distribute
It to eac= h term to clear
every denominator.
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Solving Rational Equations
Example: Suppose the value of 3/4 of an apple
and 3/5 of a coconut the same as the value of 5/6 of = a watermelon. Restate this relation in whole values.
        = ;            &n= bsp;       
LCD =3D60
(        = ;            &n= bsp;       ) *60
To restat= e a rational
equation:=
= I.Find the LCD
= II.Multiply the LCD <= /span>
to the eq= uation, distribute
It to eac= h term to clear
every denominator.
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Solving Rational Equations
Example: Suppose the value of 3/4 of an apple
and 3/5 of a coconut the same as the value of 5/6 of = a watermelon. Restate this relation in whole values.
        = ;            &n= bsp;       
LCD =3D60
(        = ;            &n= bsp;       ) *60
To restat= e a rational
equation:=
= I.Find the LCD
= II.Multiply the LCD <= /span>
to the eq= uation, distribute
It to eac= h term to clear
every denominator.
10
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Solving Rational Equations
Example: Suppose the value of 3/4 of an apple
and 3/5 of a coconut the same as the value of 5/6 of = a watermelon. Restate this relation in whole values.
        = ;            &n= bsp;       
LCD =3D60
(        = ;            &n= bsp;       ) *60
To restat= e a rational
equation:=
= I.Find the LCD
= II.Multiply the LCD <= /span>
to the eq= uation, distribute
It to eac= h term to clear
every denominator.
10
12
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Solving Rational Equations
Example: Suppose the value of 3/4 of an apple
and 3/5 of a coconut the same as the value of 5/6 of = a watermelon. Restate this relation in whole values.
        = ;            &n= bsp;       
LCD =3D60
(        = ;            &n= bsp;       ) *60
To restat= e a rational
equation:=
= I.Find the LCD
= II.Multiply the LCD <= /span>
to the eq= uation, distribute
It to eac= h term to clear
every denominator.
10
15
12
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Solving Rational Equations
Example: Suppose the value of 3/4 of an apple
and 3/5 of a coconut the same as the value of 5/6 of = a watermelon. Restate this relation in whole values.
        = ;            &n= bsp;       
LCD =3D60
(        = ;            &n= bsp;       ) *60
45 A + 36C =3D 50w
To restat= e a rational
equation:=
= I.Find the LCD
= II.Multiply the LCD <= /span>
to the eq= uation, distribute
It to eac= h term to clear
every denominator.
10
15
12
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Solving Rational Equations
------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0025.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
To solve a rational
equation:
= I.Find the LCD
= II.Multiply the LCD
to the equation, distribute
It to each term to clear
every denominator.
= III.Solve the equations,
check the answers.
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Solving Rational Equations
To solve a rational
equation:
= I.Find = the LCD
= II.Multi= ply the LCD
to the equation, distribute
It to each term to clear
every denominator.
= III.Solve= the equations,
check the answers.
Example:  Solve
 
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Solving Rational Equations
To solve a rational
equation:
= I.Find = the LCD
= II.Multi= ply the LCD
to the equation, distribute
It to each term to clear
every denominator.
= III.Solve= the equations,
check the answers.
Example:  Solve
LCD =3D (x – 1)(x + 2),
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Solving Rational Equations
To solve a rational
equation:
= I.Find the LCD
= II.Multiply the LCD
to the equation, distribute
It to each term to clear
every denominator.
= III.Solve the equations,
check the answers.
Example:  Solve
LCD =3D (x – 1)(x + 2), multiple
the LCD to the equation:
 
------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0043_image088.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh0wDFAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADS AMUAgAAAAAAAAAL/jI+py+0Po5y02osD2Lz7D4biSJbmiabqyq5GC8fyTNd2+976zvf+nPsJh8Ri LWhMKpdMJPMJjR410qr1anJit1yptgsOE7/istlGPqvXqjT7DQe543T4vI4/3/N88L4PePUXSAg1 WIiYdJjIKLTYCLnzGElJM1mJiUOVyelz2QlK8hlK+jFaigpwmkq6ygrq+soZK4tJW0t5iwupu8vY 64sIHEw4TAxofMyXrIzH3Ez3DG23OS0rbb2Gna1XzY26/S0WLu7nXQ57jj6rvm7b7p4LH887T/9r fy+cr1/M34/sH8BlAgc6K2gwGsKE1BjWc9iIHMQiEicOqWjxB8aM/z02cpS08GMYjyLRhCzJhSRK ICdXCmrpsorKmJpoKrQZZybOFDp3nujpswTQoCOGEg1h9KgpmErHMG3q6ClUT1Kn8khqFetUrVC5 NvWqFOxRsUTJBjXrE+1OtTjZ2nRLE25MuS7prrSLEm9JvSL5fvTLEXBGwRYJTzQMEbFDxQwZJ3Rs EPJAyQAp97OsD/M9zfQ4x/PsDvQ60ehIlzMtDvU31dxYZ3NtDfY02dBoN7OtDPcx3cR4B/PtC/gu 4biI1zJ+rapVHchfNWf1PFV0cMqXm7Sesjp2ltuxTC/1vZX27jDChzKfjrwV9J3Ys1Mvczz8NvLn o3CfCf87+4bq810X6t9/RQUoIFIEFrgUgoocqCAH+lXyoDwNUsTghBFGcuFDE15UYYMZRtShgh/i syGHJUZ1okYhIjhiIi3ukyJVMXa0YoEvFnKjPzNeVaOAGmQAZJBCDklkkUZGUAAAOw== ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0043_image089.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhZwAzAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQABwBf ACgAhAAAAAAAAAsIBQAABQsLDQ0LCwgFAA0IBQUICwUAAAAFCAAFCwgICwUIDQsFAA0ICAgIDQUA BQgFBQ0ICwsIDQUFCAUFAAsFBQECAwECAwECAwECAwECAwECAwECAwECAwX/ICCOZCkEwUCUbOu+ MFwY6Rrf5YEARaLYuKDwdVoMhQXGSKA6Oo+nxtPp2E2vsENAig06jN0waaY4BX5i1iORgqTF68BO C36T1k37VcsFOAZueiN8glOEIlGFIj19ikJrVgAHgI4PEYGOSAZ1AmhvkDwGkZlCWjtrjWI9KJSk Tlooqa6ztLW2t7i5uru8vb6/dg4ow8N1wMekxMrLzM3KV87R0s63wszGyNna29zd3t/g4eI3ptoz rJhv53LZBRJuPa16oMgTFCP0+AlSa55D+WFQAegHhISOID1GwVpwwN8RgFgWNiyYYxQMS+kQBcD2 MIHFLkViHMRRpYXAKxC7Y5x8MTLGgwoUF4lyYW2ZsZRYZnz00yxPCXcZ8Vlw2HEnyqExDRol4UDW IgaTkgbBOSVJ1CxLRTRdEkjAAgEQMF6Q6tKjGK9gxUpt2aImCk8ndpxzeqOmzylxQ21hudQtCish AAA7 ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0044.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
To solve a rational
equation:
= I.Find the LCD
= II.Multiply the LCD
to the equation, distribute
It to each term to clear
every denominator.
= III.Solve the equations,
check the answers.
Example:  Solve
LCD =3D (x – 1)(x + 2), multiple
the LCD to the equation:
(x – 1)(x + 2) *(        = ;            )
 
------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0044_image090.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh0wDFAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADS AMUAgAAAAAAAAAL/jI+py+0Po5y02osD2Lz7D4biSJbmiabqyq5GC8fyTNd2+976zvf+nPsJh8Ri LWhMKpdMJPMJjR410qr1anJit1yptgsOE7/istlGPqvXqjT7DQe543T4vI4/3/N88L4PePUXSAg1 WIiYdJjIKLTYCLnzGElJM1mJiUOVyelz2QlK8hlK+jFaigpwmkq6ygrq+soZK4tJW0t5iwupu8vY 64sIHEw4TAxofMyXrIzH3Ez3DG23OS0rbb2Gna1XzY26/S0WLu7nXQ57jj6rvm7b7p4LH887T/9r fy+cr1/M34/sH8BlAgc6K2gwGsKE1BjWc9iIHMQiEicOqWjxB8aM/z02cpS08GMYjyLRhCzJhSRK ICdXCmrpsorKmJpoKrQZZybOFDp3nujpswTQoCOGEg1h9KgpmErHMG3q6ClUT1Kn8khqFetUrVC5 NvWqFOxRsUTJBjXrE+1OtTjZ2nRLE25MuS7prrSLEm9JvSL5fvTLEXBGwRYJTzQMEbFDxQwZJ3Rs EPJAyQAp97OsD/M9zfQ4x/PsDvQ60ehIlzMtDvU31dxYZ3NtDfY02dBoN7OtDPcx3cR4B/PtC/gu 4biI1zJ+rapVHchfNWf1PFV0cMqXm7Sesjp2ltuxTC/1vZX27jDChzKfjrwV9J3Ys1Mvczz8NvLn o3CfCf87+4bq810X6t9/RQUoIFIEFrgUgoocqCAH+lXyoDwNUsTghBFGcuFDE15UYYMZRtShgh/i syGHJUZ1okYhIjhiIi3ukyJVMXa0YoEvFnKjPzNeVaOAGmQAZJBCDklkkUZGUAAAOw== ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0044_image091.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhZwAzAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQABwBf ACgAhAAAAAAAAAsIBQAABQsLDQ0LCwgFAA0IBQUICwUAAAAFCAAFCwgICwUIDQsFAA0ICAgIDQUA BQgFBQ0ICwsIDQUFCAUFAAsFBQECAwECAwECAwECAwECAwECAwECAwECAwX/ICCOZCkEwUCUbOu+ MFwY6Rrf5YEARaLYuKDwdVoMhQXGSKA6Oo+nxtPp2E2vsENAig06jN0waaY4BX5i1iORgqTF68BO C36T1k37VcsFOAZueiN8glOEIlGFIj19ikJrVgAHgI4PEYGOSAZ1AmhvkDwGkZlCWjtrjWI9KJSk Tlooqa6ztLW2t7i5uru8vb6/dg4ow8N1wMekxMrLzM3KV87R0s63wszGyNna29zd3t/g4eI3ptoz rJhv53LZBRJuPa16oMgTFCP0+AlSa55D+WFQAegHhISOID1GwVpwwN8RgFgWNiyYYxQMS+kQBcD2 MIHFLkViHMRRpYXAKxC7Y5x8MTLGgwoUF4lyYW2ZsZRYZnz00yxPCXcZ8Vlw2HEnyqExDRol4UDW IgaTkgbBOSVJ1CxLRTRdEkjAAgEQMF6Q6tKjGK9gxUpt2aImCk8ndpxzeqOmzylxQ21hudQtCish AAA7 ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0044_image092.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhZwAzAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAQABwBf ACgAhAAAAAAAAAsIBQAABQsLDQ0LCwgFAA0IBQUICwUAAAAFCAAFCwgICwUIDQsFAA0ICAgIDQUA BQgFBQ0ICwsIDQUFCAUFAAsFBQECAwECAwECAwECAwECAwECAwECAwECAwX/ICCOZCkEwUCUbOu+ MFwY6Rrf5YEARaLYuKDwdVoMhQXGSKA6Oo+nxtPp2E2vsENAig06jN0waaY4BX5i1iORgqTF68BO C36T1k37VcsFOAZueiN8glOEIlGFIj19ikJrVgAHgI4PEYGOSAZ1AmhvkDwGkZlCWjtrjWI9KJSk Tlooqa6ztLW2t7i5uru8vb6/dg4ow8N1wMekxMrLzM3KV87R0s63wszGyNna29zd3t/g4eI3ptoz rJhv53LZBRJuPa16oMgTFCP0+AlSa55D+WFQAegHhISOID1GwVpwwN8RgFgWNiyYYxQMS+kQBcD2 MIHFLkViHMRRpYXAKxC7Y5x8MTLGgwoUF4lyYW2ZsZRYZnz00yxPCXcZ8Vlw2HEnyqExDRol4UDW IgaTkgbBOSVJ1CxLRTRdEkjAAgEQMF6Q6tKjGK9gxUpt2aImCk8ndpxzeqOmzylxQ21hudQtCish AAA7 ------=_NextPart_01C82DF5.A2CB77A0 Content-Location: file:///C:/09764A33/5SolvingRationalEquations_files/slide0045.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Solving Rational Equations
Solving Rational Equations
To solve a rational
equation:
= I.Find the LCD
= II.Multiply the LCD
to the equation, distribute
It to each term to clear
every denominator.
= III.Solve the equations,
check the answers.
Example:  Solve
LCD =3D (x – 1)(x + 2), multiple
the LCD to the equation:
 
        = ;            &n= bsp;           
(x – 1)(x + 2) *(        = ;            )
 
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Solving Rational Equations
To solve a rational
equation:
= I.Find the LCD
= II.Multiply the LCD
to the equation, distribute
It to each term to clear
every denominator.
= III.Solve the equations,
check the answers.
Example:  Solve
LCD =3D (x – 1)(x + 2), multiple
the LCD to the equation:
 
        = ;            &n= bsp;            (x+2)        = ;            &n= bsp;          
(x – 1)(x + 2) *(        = ;            )
 
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Solving Rational Equations
To solve a rational
equation:
= I.Find the LCD
= II.Multiply the LCD
to the equation, distribute
It to each term to clear
every denominator.
= III.Solve the equations,
check the answers.
Example:  Solve
LCD =3D (x – 1)(x + 2), multiple
the LCD to the equation:
 
        = ;            &n= bsp;            (x+2)        = ;  (x–1)        = ;            &n= bsp;           
(x – 1)(x + 2) *(        = ;            )
 
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Solving Rational Equations
To solve a rational
equation:
= I.Find = the LCD
= II.Multi= ply the LCD
to the equation, distribute
It to each term to clear
every denominator.
= III.Solve= the equations,
check the answers.
Example:  Solve
LCD =3D (x – 1)(x + 2), multiple
the LCD to the equation:
 
        = ;            &n= bsp;            (x+2)        = ;  (x–1)        = ;            &n= bsp;           
(x – 1)(x + 2) *(        = ;            )
 
3(x + 2) =3D 6( x – 1)
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Solving Rational Equations
To solve a rational
equation:
= I.Find = the LCD
= II.Multi= ply the LCD