document.write( "Question 105706: Help would be great!! x-4/x-5 - 3/x+5 = 10/(x-5)(x+5)\r
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Algebra.Com's Answer #76977 by ankor@dixie-net.com(22740)\"\" \"About 
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:
\n" ); document.write( "\"%28%28x-4%29%29%2F%28%28x-5%29%29\" - \"3%2F%28%28x%2B5%29%29\" = \"10%2F%28%28x-5%29%28x%2B5%29%29\"
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\n" ); document.write( "We can get rid of the denominators if we multiply thru by (x-5)(x+5)
\n" ); document.write( "(x-5)(x+5)*\"%28%28x-4%29%29%2F%28%28x-5%29%29\" - (x-5)(x+5)*\"3%2F%28%28x%2B5%29%29\" = (x-5)(x+5)*\"10%2F%28%28x-5%29%28x%2B5%29%29\"
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\n" ); document.write( "Cancel out the denominator and you have:
\n" ); document.write( "(x+5)(x-4) - 3(x-5) = 10
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\n" ); document.write( "FOIL, then combine like terms on the left:
\n" ); document.write( "(x^2 + x - 20) - 3x + 15 = 10
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\n" ); document.write( "x^2 + x - 3x - 20 + 15 - 10 = 0
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\n" ); document.write( "x^2 - 2x - 15 = 0: a quadratic equation, we can factor
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\n" ); document.write( "(x-5)(x+3) = 0
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\n" ); document.write( "x = +5
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\n" ); document.write( "x = -3
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\n" ); document.write( "It's important to notice that x = +5 is NOT a solution, as it produces
\n" ); document.write( "division by 0 in the original equation
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\n" ); document.write( "The leaves us with a solution: x = -3
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\n" ); document.write( "Substituting -3 for x in the original equation:
\n" ); document.write( "\"%28%28-3-4%29%29%2F%28%28-3-5%29%29\" - \"3%2F%28%28-3%2B5%29%29\" = \"10%2F%28%28-3-5%29%283%2B5%29%29\"
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\n" ); document.write( "\"%28%28-7%29%29%2F%28%28-8%29%29\" - \"3%2F%28%282%29%29\" = \"10%2F%28%28-8%29%282%29%29\"
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\n" ); document.write( "\"%28%287%29%29%2F%28%288%29%29\" - \"3%2F%28%282%29%29\" = \"10%2F%28%28-16%29%29\"
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\n" ); document.write( "\"%28%2814%29%29%2F%28%2816%29%29\" - \"24%2F%28%2816%29%29\" = -\"10%2F%28%2816%29%29\"; confirms our solution
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