document.write( "Question 203563: When solving a rational equation, why is it necessary to perform a check? \n" ); document.write( "
Algebra.Com's Answer #153601 by Edwin McCravy(20056)\"\" \"About 
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When solving a rational equation, why is it necessary to perform a check?
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document.write( "In solving a rational equation, we always clear of fractions.\r\n" );
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document.write( "When we clear of fractions we always multiply both sides by a\r\n" );
document.write( "variable quantity.\r\n" );
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document.write( "When we multiply both sides of an equation by a variable expression,\r\n" );
document.write( "we may introduce an extraneous solution a zero of that expression \r\n" );
document.write( "we multiplied through by.   \r\n" );
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document.write( "Example:\r\n" );
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document.write( "\"2%2F%28x%2B2%29%2B1%2F%28x-3%29=+-10%2F%28%28x%2B2%29%28x-3%29%29\"\r\n" );
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document.write( "The LCD is \"%28x%2B2%29%28x-3%29\"\r\n" );
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document.write( "So we multiply through by \"%28%28x%2B2%29%28x-3%29%29%2F1\"\r\n" );
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document.write( "\"2%28x-3%29%2B%28x%2B2%29=-10\"\r\n" );
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document.write( "\"2x-6%2Bx%2B2=-10\"\r\n" );
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document.write( "\"3x-4=-10\"\r\n" );
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document.write( "\"3x=-6\"\r\n" );
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document.write( "\"x=-6%2F3\"\r\n" );
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document.write( "\"x=-2\"\r\n" );
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document.write( "So at first it appears that \"x=-2\" is\r\n" );
document.write( "a solution.  However when we check:\r\n" );
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document.write( "\"2%2F%28x%2B2%29%2B1%2F%28x-3%29=+-10%2F%28%28x%2B2%29%28x-3%29%29\"\r\n" );
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document.write( "\"2%2F0%2B1%2F%28-5%29=+-10%2F%280%29%28-5%29%29\"\r\n" );
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document.write( "\"2%2F0%2B1%2F%28-5%29=+-10%2F0%29\"\r\n" );
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document.write( "But there are zeros in two denominators!\r\n" );
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document.write( "So there is no solution to this rational equation.\r\n" );
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document.write( "Edwin
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