document.write( "Question 239853: Solve x+5/x^2+x = 1/x^2+x - x-6/x+1. \n" ); document.write( "
Algebra.Com's Answer #175933 by algebrapro18(249)\"\" \"About 
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Solve \"%28x%2B5%29%2F%28x%5E2%2Bx%29+=+1%2F%28x%5E2%2Bx%29+-+%28x-6%29%2F%28x%2B1%29\"
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\n" ); document.write( "\n" ); document.write( "First we need to factor the denominator of the above problem.
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\n" ); document.write( "\n" ); document.write( "\"%28x%2B5%29%2F%28x%5E2%2Bx%29+=+1%2F%28x%5E2%2Bx%29+-+%28x-6%29%2F%28x%2B1%29\"
\n" ); document.write( "= \"%28x%2B5%29%2F%28x%28x%2B1%29%29+=+1%2F%28x%28x%2B1%29%29+-+%28x-6%29%2F%28x%2B1%29\"
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\n" ); document.write( "\n" ); document.write( "Now we find a common denominator. It will be x(x+1). Now multiply the origonal equation by x(x+1) and simplify.
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\n" ); document.write( "\n" ); document.write( "\"%28x%2B5%29%2F%28x%28x%2B1%29%29+=+1%2F%28x%28x%2B1%29%29+-+%28x-6%29%2F%28x%2B1%29\"
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\n" ); document.write( "\"x%2B5+=+1+-+%28x%29%28x-6%29\"
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\n" ); document.write( "\n" ); document.write( "Now we solve for x.
\n" ); document.write( "x+5 = 1 - (x)(x-6)
\n" ); document.write( "x+5 = 1 - x^2+6x
\n" ); document.write( "x^2-6x+x+5-1 = 0
\n" ); document.write( "x^2-5x+4 = 0
\n" ); document.write( "(x-4)(x-1) = 0
\n" ); document.write( "x = 4 and x = 1
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