document.write( "Question 1179019: The rational expression (x^2+9x+k)/(x^2+5x-6), x is NOT equal to 1, -6 simplifies to (x+3)/(x-1) because k equals .... \n" ); document.write( "
Algebra.Com's Answer #808508 by Edwin McCravy(20063)\"\" \"About 
You can put this solution on YOUR website!
The rational expression (x^2+9x+k)/(x^2+5x-6), x is NOT equal to 1, -6 simplifies to (x+3)/(x-1) because k equals ....
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document.write( "\"%28x%5E2%2B9x%2Bk%29%2F%28x%5E2%2B5x-6%29\" will simplify to \"%28x%2B3%29%2F%28x-1%29\" if and only if \r\n" );
document.write( "every value of x (other than 1 and -6) when substituted in both, gives the\r\n" );
document.write( "same result.  Therefore, since 0 is the easiest possible number to substitute\r\n" );
document.write( "for x, let's use it. [But any other number (other than 1 and -6) will work\r\n" );
document.write( "just as well.  It just won't be as easy.]\r\n" );
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document.write( "Substituting x=0 in\r\n" );
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document.write( "\"%28x%5E2%2B9x%2Bk%29%2F%28x%5E2%2B5x-6%29\" gives\r\n" );
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document.write( "\"%28%280%29%5E2%2B9%280%29%2Bk%29%2F%28%280%29%5E2%2B5%280%29-6%29\"\r\n" );
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document.write( "which reduces to\r\n" );
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document.write( "\"k%2F%28-6%29\"\r\n" );
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document.write( "Substituting x=0 in \"%28x%2B3%29%2F%28x-1%29\" gives\r\n" );
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document.write( "\"%28%280%29%2B3%29%2F%28%280%29-1%29\" \r\n" );
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document.write( "which reduces to\r\n" );
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document.write( "\"%283%29%2F%28-1%29\" \r\n" );
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document.write( "or \r\n" );
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document.write( "\"-3\"\r\n" );
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document.write( "Setting those equal:\r\n" );
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document.write( "\"k%2F%28-6%29\"\"%22%22=%22%22\"\"-3\"\r\n" );
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document.write( "\"k\"\"%22%22=%22%22\"\"18\"   <--ANSWER\r\n" );
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document.write( "Check by substituting k=18 in\r\n" );
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document.write( "\"%28x%5E2%2B9x%2Bk%29%2F%28x%5E2%2B5x-6%29\"\r\n" );
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document.write( "\"%28x%5E2%2B9x%2B18%29%2F%28x%5E2%2B5x-6%29\"\r\n" );
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document.write( "Factoring numerator and denominator:\r\n" );
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document.write( "\"%28%28x%2B3%29%28x%2B6%29%29%2F%28%28x%2B6%29%28x-1%29%29\"\r\n" );
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document.write( "Canceling:\r\n" );
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document.write( "\"%28%28x%2B3%29%28cross%28x%2B6%29%29%29%2F%28%28cross%28x%2B6%29%29%28x-1%29%29\"\r\n" );
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document.write( "So it reduces to:\r\n" );
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document.write( "\"%28x%2B3%29%2F%28x-1%29\"\r\n" );
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document.write( "Edwin
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