document.write( "Question 621492: 9 divided by the difference of a number and 1 minus 8 divided by a number plus 1, equals 9 times the reciprocal of the difference of the number squared 1. \n" ); document.write( "

Algebra.Com's Answer #390793 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Let n = \"a number\"
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\n" ); document.write( "Assume the statement is:
\n" ); document.write( "\"9 divided by the difference of a number and 1 minus 8 divided by a number plus 1, equals 9 times the reciprocal of the difference of the number squared and 1.\"
\n" ); document.write( ":
\n" ); document.write( " $\"9%2F%28%28n-1%29%29\"$ - $\"8%2F%28%28n%2B1%29%29\"$ = 9( $\"1%2F%28%28n%5E2-1%29%29\"$ )
\n" ); document.write( "we can factor the 3rd denominator, as the \"difference of squares\"
\n" ); document.write( " $\"9%2F%28%28n-1%29%29\"$ - $\"8%2F%28%28n%2B1%29%29\"$ = 9( $\"1%2F%28%28n-1%29%28n%2B1%29%29\"$ )
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\n" ); document.write( "multiply by (x+1)(x-1), results gets rid of the denominators and we have
\n" ); document.write( "9(n+1) - 8(n-1) = 9
\n" ); document.write( "9n + 9 - 8n + 8 = 9
\n" ); document.write( "9n - 8n = 9 - 17
\n" ); document.write( "n = -8
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\n" ); document.write( "Check this replace n with -8
\n" ); document.write( " $\"9%2F%28%28-8-1%29%29\"$ - $\"8%2F%28%28-8%2B1%29%29\"$ = 9( $\"1%2F%28%28-8%5E2-1%29%29\"$ )
\n" ); document.write( " $\"9%2F%28-9%29\"$ - $\"8%2F%28-7%29\"$ = 9( $\"1%2F%28%2864-1%29%29\"$ )
\n" ); document.write( " $\"-1\"$ + $\"8%2F7\"$ = $\"9%2F63\"$
\n" ); document.write( "-1 + $\"8%2F7\"$ = $\"1%2F7\"$ \n" ); document.write( "

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