document.write( "Question 1075068: 6 divided by the difference of a number and 2, minus 5 divided by a number plus 2, equals 5 times the reciprocal of the difference of the number squared and 4. What is the number? \n" ); document.write( "

Algebra.Com's Answer #689763 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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6 divided by the difference of a number and 2, minus 5 divided by a number plus 2, equals 5 times the reciprocal of the difference of the number squared and 4. What is the number?
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\n" ); document.write( " $\"6%2F%28%28x-2%29%29+-+5%2F%28%28x%2B2%29%29+=+5%281%2F%28%28x%5E2-4%29%29%29\"$
\n" ); document.write( "we know that (x-2)(x+2) = x^2-4
\n" ); document.write( "multiply equation by x^2-4, cancel the denominators, then we have\r
\n" ); document.write( "\n" ); document.write( "6(x+2) - 5(x-2) = 5
\n" ); document.write( "6x + 12 - 5x + 10 = 5
\n" ); document.write( "6x - 5x + 22 = 5
\n" ); document.write( "x = 5 - 22
\n" ); document.write( "x = -17
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\n" ); document.write( "See if that checks out
\n" ); document.write( " $\"6%2F%28%28-17-2%29%29+-+5%2F%28%28-17%2B2%29%29+=+5%281%2F%28%28-17%5E2-4%29%29%29\"$
\n" ); document.write( " $\"6%2F%28-19%29+-+5%2F%28-15%29+=+5%281%2F%28289-4%29%29\"$
\n" ); document.write( " $\"-6%2F19+%2B+5%2F15+=+5%2F285\"$ Checks out on a my calc\r
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