document.write( "Question 1179209: Resolve 3x²+1/(x-2)²(x²+2x+2) to partial fraction \n" ); document.write( "
Algebra.Com's Answer #808740 by Edwin McCravy(20062)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The other tutor did not understand.  \r\n" );
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document.write( "\"%283x%5E2%2B1%29%2F%28%28x-2%5E%22%22%29%5E2%28x%5E2%2B2x%2B2%29%29\"\"%22%22=%22%22\"\"A%5E%22%22%2F%28x%5E%22%22%2B2%5E%22%22%5E%22%22%29\"\"%22%22%2B%22%22\"\"B%5E%22%22%2F%28x%5E%22%22%2B2%29%5E2\"\"%22%22%2B%22%22\"\"%28Cx%5E%22%22%5E%22%22%2BD%29%2F%28x%5E2%5E%22%22%2B2x%2B2%29\"\r\n" );
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document.write( "Multiply by the LCD\r\n" );
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document.write( "\"3x%5E2%2B1\"\"%22%22=%22%22\"\"A%28x%5E%22%22%2B2%29%28x%5E2%2B2x%2B2%29\"\"%22%22%2B%22%22\"\"B%28x%5E2%2B2x%2B2%29\"\"%22%22%2B%22%22\"\"%28Cx%5E%22%22%2BD%29%28x%5E%22%22%2B2%29%5E2\"\r\n" );
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document.write( "Since this must be an identity, we can substitute any numbers for x.\r\n" );
document.write( "Substitute x=-2  (I chose -2 to make some terms become 0) \r\n" );
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document.write( "\"3%28-2%29%5E2%2B1\"\"%22%22=%22%22\"\"A%28%28-2%29%5E%22%22%2B2%29%28%28-2%29%5E2%2B2%28-2%29%2B2%29\"\"%22%22%2B%22%22\"\"B%28%28-2%29%5E2%2B2%28-2%29%2B2%29\"\"%22%22%2B%22%22\"\"%28C%28-2%29%5E%22%22%2BD%29%28%28-2%29%5E%22%22%2B2%29%5E2\"\r\n" );
document.write( "\"13\"\"%22%22=%22%22\"\"2B\"\r\n" );
document.write( "\"13%2F2\"\"%22%22=%22%22\"\"B\"\r\n" );
document.write( "\r\n" );
document.write( "\"3x%5E2%2B1\"\"%22%22=%22%22\"\"A%28x%5E%22%22%2B2%29%28x%5E2%2B2x%2B2%29\"\"%22%22%2B%22%22\"\"%2813%2F2%29%28x%5E2%2B2x%2B2%29\"\"%22%22%2B%22%22\"\"%28Cx%5E%22%22%2BD%29%28x%5E%22%22%2B2%29%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"6x%5E2%2B2\"\"%22%22=%22%22\"\"2A%28x%5E%22%22%2B2%29%28x%5E2%2B2x%2B2%29\"\"%22%22%2B%22%22\"\"13%28x%5E2%2B2x%2B2%29\"\"%22%22%2B%22%22\"\"2%28Cx%5E%22%22%2BD%29%28x%5E%22%22%2B2%29%5E2\"\r\n" );
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document.write( "Substitute x=0  (I chose that because it's easy to substitute)\r\n" );
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document.write( "\"6%280%29%5E2%2B2\"\"%22%22=%22%22\"\"2A%28%280%29%5E%22%22%2B2%29%28%280%29%5E2%2B2%280%29%2B2%29\"\"%22%22%2B%22%22\"\"13%28%280%29%5E2%2B2%280%29%2B2%29\"\"%22%22%2B%22%22\"\"2%28C%280%29%5E%22%22%2BD%29%28%280%29%5E%22%22%2B2%29%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"2\"\"%22%22=%22%22\"\"2A%282%29%282%29%29\"\"%22%22%2B%22%22\"\"13%282%29\"\"%22%22%2B%22%22\"\"2%28D%29%282%29%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"2\"\"%22%22=%22%22\"\"8A\"\"%22%22%2B%22%22\"\"26\"\"%22%22%2B%22%22\"\"8D\"\r\n" );
document.write( "\r\n" );
document.write( "\"-24\"\"%22%22=%22%22\"\"8A\"\"%22%22%2B%22%22\"\"8D\"\r\n" );
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document.write( "\"-3\"\"%22%22=%22%22\"\"A\"\"%22%22%2B%22%22\"\"D\"\r\n" );
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document.write( "Substitute D = -A - 3\r\n" );
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document.write( "\"6x%5E2%2B2\"\"%22%22=%22%22\"\"2A%28x%5E%22%22%2B2%29%28x%5E2%2B2x%2B2%29\"\"%22%22%2B%22%22\"\"13%28x%5E2%2B2x%2B2%29\"\"%22%22%2B%22%22\"\"2%28Cx%5E%22%22-A-3%29%28x%5E%22%22%2B2%29%5E2\"\r\n" );
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document.write( "Substitute x=1  \r\n" );
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document.write( "\"6%281%29%5E2%2B2\"\"%22%22=%22%22\"\"2A%28%281%29%5E%22%22%2B2%29%28%281%29%5E2%2B2%281%29%2B2%29\"\"%22%22%2B%22%22\"\"13%28%281%29%5E2%2B2%281%29%2B2%29\"\"%22%22%2B%22%22\"\"2%28C%281%29%5E%22%22-A-3%29%28%281%29%5E%22%22%2B2%29%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"8\"\"%22%22=%22%22\"\"2A%283%29%285%29\"\"%22%22%2B%22%22\"\"13%285%29\"\"%22%22%2B%22%22\"\"2%28C-A-3%29%283%29%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"8\"\"%22%22=%22%22\"\"30A\"\"%22%22%2B%22%22\"\"65\"\"%22%22%2B%22%22\"\"2%28C-A-3%29%289%29\"\r\n" );
document.write( "\"8\"\"%22%22=%22%22\"\"30A\"\"%22%22%2B%22%22\"\"65\"\"%22%22%2B%22%22\"\"18%28C-A-3%29\"\r\n" );
document.write( "\"8\"\"%22%22=%22%22\"\"30A\"\"%22%22%2B%22%22\"\"65\"\"%22%22%2B%22%22\"\"18C-18A-54%29\"\r\n" );
document.write( "\"8\"\"%22%22=%22%22\"\"12A\"\"%22%22%2B%22%22\"\"11\"\"%22%22%2B%22%22\"\"18C%29\"\r\n" );
document.write( "\"8\"\"%22%22=%22%22\"\"12A\"\"%22%22%2B%22%22\"\"11\"\"%22%22%2B%22%22\"\"18C%29\"\r\n" );
document.write( "\"-3\"\"%22%22=%22%22\"\"12A\"\"%22%22%2B%22%22\"\"18C%29\"\r\n" );
document.write( "\"-1\"\"%22%22=%22%22\"\"4A\"\"%22%22%2B%22%22\"\"6C%29\"\r\n" );
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document.write( "Substitute x=-1  \r\n" );
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document.write( "\"6%28-1%29%5E2%2B2\"\"%22%22=%22%22\"\"2A%28%28-1%29%5E%22%22%2B2%29%28%28-1%29%5E2%2B2%28-1%29%2B2%29\"\"%22%22%2B%22%22\"\"13%28%28-1%29%5E2%2B2%28-1%29%2B2%29\"\"%22%22%2B%22%22\"\"2%28C%28-1%29%5E%22%22-A-3%29%28%28-1%29%5E%22%22%2B2%29%5E2\"\r\n" );
document.write( "\r\n" );
document.write( "\"8\"\"%22%22=%22%22\"\"2A%281%29%281%29\"\"%22%22%2B%22%22\"\"13%281%29\"\"%22%22%2B%22%22\"\"2%28-C-A-3%29%281%29%5E2\"\r\n" );
document.write( "\"8\"\"%22%22=%22%22\"\"2A\"\"%22%22%2B%22%22\"\"13\"\"%22%22%2B%22%22\"\"2%28-C-A-3%29\"\r\n" );
document.write( "\"8\"\"%22%22=%22%22\"\"2A\"\"%22%22%2B%22%22\"\"13\"\"%22%22-%22%22\"\"2C-2A-6%29\"\r\n" );
document.write( "\"8\"\"%22%22=%22%22\"\"-2C\"\"%22%22%2B%22%22\"\"7\"\r\n" );
document.write( "\"1\"\"%22%22=%22%22\"\"-2C\"\r\n" );
document.write( "\"-1%2F2\"\"%22%22=%22%22\"\"C\"\r\n" );
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document.write( "Substitute C = -1/2 in\r\n" );
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document.write( "\"-1\"\"%22%22=%22%22\"\"4A\"\"%22%22%2B%22%22\"\"6C%29\"\r\n" );
document.write( "\"-1\"\"%22%22=%22%22\"\"4A\"\"%22%22%2B%22%22\"\"6%28-1%2F2%29%29\"\r\n" );
document.write( "\"-1\"\"%22%22=%22%22\"\"4A\"\"%22%22-%22%22\"\"3%29\"\r\n" );
document.write( "\"2\"\"%22%22=%22%22\"\"4A\"\r\n" );
document.write( "\"2%2F4\"\"%22%22=%22%22\"\"A\"\r\n" );
document.write( "\"1%2F2\"\"%22%22=%22%22\"\"A\"\r\n" );
document.write( "\r\n" );
document.write( "Substitute A = 1/2 in \r\n" );
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document.write( "\"D\"\"%22%22=%22%22\"\"-A+-+3\"\r\n" );
document.write( "\"D\"\"%22%22=%22%22\"\"-1%2F2+-+3\"\r\n" );
document.write( "\"D\"\"%22%22=%22%22\"\"-1%2F2+-+6%2F2\"\r\n" );
document.write( "\"D\"\"%22%22=%22%22\"\"-7%2F2\"\r\n" );
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document.write( "Substituting all the capital letters we've found:\r\n" );
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document.write( "\"%283x%5E2%2B1%29%2F%28%28x-2%5E%22%22%29%5E2%28x%5E2%2B2x%2B2%29%29\"\"%22%22=%22%22\"\"1%5E%22%22%2F%282%28x%5E%22%22%2B2%5E%22%22%5E%22%22%29%29\"\"%22%22%2B%22%22\"\"13%5E%22%22%2F%282%28x%5E%22%22%2B2%29%5E2%29\"\"%22%22%2B%22%22\"\"%28%28-1%2F2%29x%5E%22%22%5E%22%22%2B%28-7%2F2%29%29%2F%28x%5E2%5E%22%22%2B2x%2B2%29\"\r\n" );
document.write( " \r\n" );
document.write( "So the final answer is:\r\n" );
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document.write( "\"%283x%5E2%2B1%29%2F%28%28x-2%5E%22%22%29%5E2%28x%5E2%2B2x%2B2%29%29\"\"%22%22=%22%22\"\"1%5E%22%22%2F%282%28x%5E%22%22%2B2%5E%22%22%29%29\"\"%22%22%2B%22%22\"\"13%5E%22%22%2F%282%28x%5E%22%22%2B2%29%5E2%29\"\"%22%22-%22%22\"\"%28x%5E%22%22%5E%22%22%2B7%29%2F%282%28x%5E2%2B2x%2B2%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
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