document.write( "Question 1205608: Let f(x) = (x^2 + 7x - 6)/(x-1)(x-2)(x+1)
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Algebra.Com's Answer #842536 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "You should have grouped the factors in the denominator\r\n" );
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document.write( " f(x) = (x^2 + 7x - 6)/[(x-1)(x-2)(x+1)]\r\n" );
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document.write( "\"f%28x%29+=%28x%5E2+%2B+7x+-+6%5E%22%22%29%2F%28%28x-1%29%28x-2%29%28x%2B1%29%5E%22%22%29\"\"%22==%22\"\"A%2F%28x-1%29%2BB%2F%28x-2%29%2BC%2F%28x%2B1%29\"\r\n" );
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document.write( "Multiply through by (x-1)(x-2)(x+1)\r\n" );
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document.write( "\"f%28x%29+=x%5E2%2B7x-6\"\"%22==%22\"\"A%28x-2%29%28x%2B1%29%2BB%28x-1%29%28x%2B1%29%2BC%28x-1%29%28x-2%29\"\r\n" );
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document.write( "Substituting x=2 will cause two of the terms on the right to become 0, \r\n" );
document.write( "then you can solve for B = -2\r\n" );
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document.write( "Substituting x=-1 will also cause two of the terms on the right to become 0, \r\n" );
document.write( "then you can solve for C = 4\r\n" );
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document.write( "Substituting x=1 will also cause two of the terms on the right to become 0, \r\n" );
document.write( "then you can solve for A = -1\r\n" );
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document.write( "\"f%28x%29+=-expr%281%2F%28x-1%29%29-expr%282%2F%28x%2B1%29%29%2B4%2F%28x-2%29\"  \r\n" );
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document.write( "Those terms look similar to the sum of an infinite geometric series:\r\n" );
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document.write( "\"f%28x%29+=a%2F%281-r%29\"\"%22%22=%22%22\"\"a%2Bar%2Bar%5E2%2Bar%5E3%2B%22%22%2A%22%22%2A%22%22%2A%22%22\"\"%22%22=%22%22\"\"a%281%2Br%2Br%5E2%2Br%5E3%2B%22%22%2A%22%22%2A%22%22%2A%22%22%29\"\r\n" );
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document.write( "We can get the first term in that form:\r\n" );
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document.write( "\"-1%2F%28x-1%29=1%2F%28-x%2B1%29=1%2F%281-x%29\"\r\n" );
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document.write( "We can get the second term in that form:\r\n" );
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document.write( "\"-2%2F%28x%2B1%29=-2%2F%281%2Bx%29=-2%2F%281-%28-x%29%29\"\r\n" );
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document.write( "The third term needs to have first term 1 in the denominator:\r\n" );
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document.write( "\"4%2F%28x-2%29=-4%2F%282-x%29=-4%2F%282%281-%22x%2F2%22%29%29=-2%2F%281-%22x%2F2%22%29\"\r\n" );
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document.write( "So we have:\r\n" );
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document.write( "\"f%28x%29+=1%2F%281-x%29-2%2F%281-%28-x%29%29-2%2F%281-%22x%2F2%22%29\"\r\n" );
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document.write( "Using the above equation for \"a%2F%281-r%29\" on each term:\r\n" );
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document.write( "Simplifying that gives\r\n" );
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document.write( "Simplifying and omitting terms in x4 and higher we have:\r\n" );
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document.write( "\"f%28x%29+=-3+%2B+2x+-+expr%283%2F2%29+x%5E2+%2B+expr%2811%2F4%29x%5E3\"\r\n" );
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document.write( "Edwin
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