document.write( "Question 390385: Adding Rational Expressions\r
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Algebra.Com's Answer #277007 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Add:\r\n" );
document.write( "\"3%2F%28x%5E3-x%29\"\"%22%22%2B%22%22\"\"4%2F%28x%5E2%2B2x%2B1%29\"\r\n" );
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document.write( "Factor the first denominator completely:\r\n" );
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document.write( "\"x%5E3-x\"\"%22%22=%22%22\"\"x%28x%5E2-1%29\"\"%22%22=%22%22\"\"x%28x-1%29%28x%2B1%29\"\r\n" );
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document.write( "Factor the second denominator completely:\r\n" );
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document.write( "\"x%5E2%2B2x%2B1\"\"%22%22=%22%22\"\"%28x%2B1%29%28x%2B1%29\"\"%22%22=%22%22\"\"%28x%2B1%29%5E2\"\r\n" );
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document.write( "\"3%2F%28x%28x-1%29%28x%2B1%29%29\"\"%22%22%2B%22%22\"\"4%2F%28x%2B1%29%5E2\"\r\n" );
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document.write( "Creating the LCD:\r\n" );
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document.write( "Rule:\r\n" );
document.write( "The LCD must contain each factor of each denominator to the largest power\r\n" );
document.write( "it appears in any denominator.\r\n" );
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document.write( "The factor \"x\" occurs to the first power in the first fraction,\r\n" );
document.write( "and not at all in the second fraction, so the LCD will contain \"x\"\r\n" );
document.write( "to the first power.\r\n" );
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document.write( "The factor \"%28x-1%29\" occurs to the first power in the first fraction,\r\n" );
document.write( "and not at all in the second fraction, so the LCD will contain \"%28x-1%29\"\r\n" );
document.write( "to the first power.\r\n" );
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document.write( "The factor \"%28x%2B1%29\" occurs to the first power in the first fraction,\r\n" );
document.write( "and to the 2nd power in the second fraction, so the LCD will contain \r\n" );
document.write( "\"%28x%2B1%29\" to the 2nd power, or \"%28x%2B1%29%5E2\"\r\n" );
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document.write( "Therefore the LCD = \"x%28x-1%29%28x%2B1%29%5E2\"\r\n" );
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document.write( "\"3%2F%28x%28x-1%29%28x%2B1%29%29\"\"%22%22%2B%22%22\"\"4%2F%28x%2B1%29%5E2\"\r\n" );
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document.write( "The first fraction needs to be multiplied by \"red%28%28%28x%2B1%29%29%2F%28%28x%2B1%29%29%29\" so that\r\n" );
document.write( "its denominator will become the LCD:\r\n" );
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document.write( "\"%22%22%2B%22%22\"\"4%2F%28x%2B1%29%5E2\"\r\n" );
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document.write( "The second fraction needs to be multiplied by \"red%28++%28x%28x-1%29%29%2F%28x%28x-1%29%29++%29\"\r\n" );
document.write( "so that its denominator will also become the LCD:\r\n" );
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document.write( "\"%22%22%2B%22%22\"\r\n" );
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document.write( "\"++%283%28x%2B1%29%29%2F%28x%28x-1%29%28x%2B1%29%5E2%29\"\"%22%22%2B%22%22\"\"%284x%28x-1%29%29%2F%28x%28x-1%29%28x%2B1%29%5E2%29\"\r\n" );
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document.write( "Multiply the numerators out but do not multiply the\r\n" );
document.write( "denominators out.\r\n" );
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document.write( "\"++%283x%2B3%29%2F%28x%28x-1%29%28x%2B1%29%5E2%29\"\"%22%22%2B%22%22\"\"%284x%5E2-4x%29%2F%28x%28x-1%29%28x%2B1%29%5E2%29\"\r\n" );
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document.write( "Combine the numerators over the LCD:\r\n" );
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document.write( "\"%283x%2B3%2B4x%5E2-4x%29%2F%28x%28x-1%29%28x%2B1%29%5E2%29\"\r\n" );
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document.write( "\"%284x%5E2-x%2B3%29%2F%28x%28x-1%29%28x%2B1%29%5E2%29\"\r\n" );
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document.write( "The numerator doesn't factor, so we leave it like that.\r\n" );
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document.write( "Edwin
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