document.write( "Question 78353: Homework example. Please help me understand and show me how to solve this complex fraction. Thanks!\r
\n" ); document.write( "\n" ); document.write( "3/x-2 + 21/x^2-4 = 14/x+2\r
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Algebra.Com's Answer #56194 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
I assume you mean; (a few brackets would help remove all doubt)
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\n" ); document.write( "\"3%2F%28%28x-2%29%29\" + \"21%2F%28%28x%5E2-4%29%29\" = \"14%2F%28%28x%2B2%29%29\"
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\n" ); document.write( "Notice that (x^2 - 4) is the difference of squares, can be factored to:
\n" ); document.write( "\"3%2F%28%28x-2%29%29\" + \"21%2F%28%28x-2%29%28x%2B2%29%29\" = \"14%2F%28%28x%2B2%29%29\"
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\n" ); document.write( "If we multiply thru by (x-2)(x+2) we have:
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\n" ); document.write( "3(x+2) + 21 = 14(x-2)
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\n" ); document.write( "Multiply what's inside the brackets and do some basic algebra:
\n" ); document.write( "3x + 6 + 21 = 14x - 28
\n" ); document.write( "3x + 27 = 14x - 28
\n" ); document.write( "3x - 14x = -28 - 27
\n" ); document.write( "-11x = -55
\n" ); document.write( "x = -55/-11
\n" ); document.write( "x = +5
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\n" ); document.write( "Check our solution of x=5 for equality in the original equation:
\n" ); document.write( "\"3%2F%28%285-2%29%29\" + \"21%2F%28%285%5E2-4%29%29\" = \"14%2F%28%285%2B2%29%29\"
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\n" ); document.write( "\"3%2F%28%283%29%29\" + \"21%2F%28%2821%29%29\" = \"14%2F%28%287%29%29\"; confirms our solution
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\n" ); document.write( "How about this? Did you understand what went on here?
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