document.write( "Question 1043286: Perform the long division and write the partial fraction decomposition of the remainder term. \r
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Algebra.Com's Answer #658413 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "To do the division we insert all the necessary\r\n" );
document.write( "zero place holders for all the missing powers\r\n" );
document.write( "of x.  It isn't necessary to put in the 1\r\n" );
document.write( "coefficients but I thought I'd do it anyway:\r\n" );
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document.write( "        \r\n" );
document.write( "                1x³+0x²+1x+0\r\n" );
document.write( "1x²+0x-1)1x⁵+0x⁴+0x³+0x²+0x+2\r\n" );
document.write( "         1x⁵+0x⁴-1x³\r\n" );
document.write( "             0x⁴+1x³+0x²\r\n" );
document.write( "             0x⁴+0x³+0x²\r\n" );
document.write( "                 1x³+0x²+0x\r\n" );
document.write( "                 1x³+0x²-1x\r\n" );
document.write( "                     0x²+1x+2\r\n" );
document.write( "                     0x²+0x+0\r\n" );
document.write( "                         1x+2\r\n" );
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document.write( "So \r\n" );
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document.write( "\"%28x%5E5%2B2%29%2F%28x%5E2-1%29\"\"%22%22=%22%22\"\"x%5E3%2Bx%2B%28x%2B2%29%2F%28x%5E2-1%29\"\r\n" );
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document.write( "Now we break the fraction part into partial fractions:\r\n" );
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document.write( "First factor the denominator:\r\n" );
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document.write( "\"%28x%2B2%29%2F%28x%5E2-1%29\"\"%22%22=%22%22\"\"%28x%2B2%29%2F%28%28x-1%29%28x%2B1%29%29\"\r\n" );
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document.write( "Then\r\n" );
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document.write( "\"%28x%2B2%29%2F%28%28x-1%29%28x%2B1%29%29\"\"%22%22=%22%22\"\"A%2F%28x-1%29%2BB%2F%28x%2B1%29\"\r\n" );
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document.write( "Multiply through by the LCD = (x-1)(x+1)\r\n" );
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document.write( "\"x%2B2\"\"%22%22=%22%22\"\"A%28x%2B1%29%2BB%28x-1%29\"\r\n" );
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document.write( "This must be true for all values of x.\r\n" );
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document.write( "So substitute x=1 to make the last term on the right\r\n" );
document.write( "become 0: \r\n" );
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document.write( "\"1%2B2\"\"%22%22=%22%22\"\"A%281%2B1%29%2BB%281-1%29\"\r\n" );
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document.write( "\"3\"\"%22%22=%22%22\"\"2A\"\r\n" );
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document.write( "\"3%2F2\"\"%22%22=%22%22\"\"A\"\r\n" );
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document.write( "Substitute x=-1 to make the first term on the right\r\n" );
document.write( "become 0:\r\n" );
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document.write( "\"-1%2B2\"\"%22%22=%22%22\"\"A%28-1%2B1%29%2BB%28-1-1%29\"\r\n" );
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document.write( "\"1\"\"%22%22=%22%22\"\"-2B\"\r\n" );
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document.write( "\"-1%2F2\"\"%22%22=%22%22\"\"B\"\r\n" );
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document.write( "So \r\n" );
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document.write( "\"%28x%2B2%29%2F%28%28x-1%29%28x%2B1%29%29\"\"%22%22=%22%22\"\"A%2F%28x-1%29%2BB%2F%28x%2B1%29\"\r\n" );
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document.write( "becomes:\r\n" );
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document.write( "\"%28x%2B2%29%2F%28%28x-1%29%28x%2B1%29%29\"\"%22%22=%22%22\"\"%223%2F2%22%2F%28x-1%29%2B%22-1%2F2%22%2F%28x%2B1%29\"\r\n" );
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document.write( "Simplify those by multiplying tops and bottoms by 2\r\n" );
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document.write( "\"%28x%2B2%29%2F%28%28x-1%29%28x%2B1%29%29\"\"%22%22=%22%22\"\"3%2F%282%28x-1%29%29-1%2F%282%28x%2B1%29%29\"\r\n" );
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document.write( "Substituting in\r\n" );
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document.write( "\"%28x%5E5%2B2%29%2F%28x%5E2-1%29\"\"%22%22=%22%22\"\"x%5E3%2Bx%2B%28x%2B2%29%2F%28x%5E2-1%29\" \r\n" );
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document.write( "\"%28x%5E5%2B2%29%2F%28x%5E2-1%29\"\"%22%22=%22%22\"\"x%5E3%2Bx%2B3%2F%282%28x-1%29%29-1%2F%282%28x%2B1%29%29\"    \r\n" );
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document.write( "Edwin
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