document.write( "Question 442607: x/(x-6)-6/(x+6)=72/(x^2-36) \n" ); document.write( "
Algebra.Com's Answer #305310 by swincher4391(1107)\"\" \"About 
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\"x%2F%28x-6%29-6%2F%28x%2B6%29=72%2F%28x%5E2-36%29\"\r
\n" ); document.write( "\n" ); document.write( "Notice \"x%5E2-36+=++%28x%2B6%29%28x-6%29\"\r
\n" ); document.write( "\n" ); document.write( "Then \"x%2F%28x-6%29+-+6%2F%28x%2B6%29+=+72%2F%28%28x%2B6%29%28x-6%29%29\"\r
\n" ); document.write( "\n" ); document.write( "What will our common denominator be between these three denominators? (x+6)(x-6), right.\r
\n" ); document.write( "\n" ); document.write( "So we can rewrite \"x%2F%28x-6%29+=+x%28x%2B6%29%2F%28x-6%29%28x%2B6%29\"\r
\n" ); document.write( "\n" ); document.write( "Similarly we can rewrite \"6%2F%28x%2B6%29+=+6%28x-6%29%2F%28x%2B6%29%28x-6%29\"\r
\n" ); document.write( "\n" ); document.write( "So now we have \"%28x%2A%28x%2B6%29+-+6%28x-6%29%29%2F%28x%2B6%29%28x-6%29+=+72%2F%28x%2B6%29%28x-6%29\"\r
\n" ); document.write( "\n" ); document.write( "Now we can solve solely for the numerator.\r
\n" ); document.write( "\n" ); document.write( "\"x%5E2+%2B+6x+-+6x+%2B36+=+x%5E2+%2B+36+=+72\"
\n" ); document.write( "\"x%5E2+=+36\"\r
\n" ); document.write( "\n" ); document.write( "So \"x+=+6\" and \"x=-6\"\r
\n" ); document.write( "\n" ); document.write( "But wait! We need to check if these solutions are extraneous. A solution is extraneous if it makes the expression undefined. (AKA: division by 0)\r
\n" ); document.write( "\n" ); document.write( "Our denominator is (x+6)(x-6), so it is 0 when x =6 or x=-6.\r
\n" ); document.write( "\n" ); document.write( "So both x=6 and x=-6 are EXTRANEOUS! \r
\n" ); document.write( "\n" ); document.write( "Thus there is no solution.\r
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