document.write( "Question 18802: In order for the identity $\"1%2F%28x%2B1%29%2Ba%2F%28x-1%29=%28-2%29%2F%28x%5E2-1%29\"$ to hold for all x, a must equal ? \n" ); document.write( "

Algebra.Com's Answer #9024 by Earlsdon(6294) $\"\"$ $\"About$

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Here's one approach:\r
\n" ); document.write( "\n" ); document.write( " $\"1%2F%28x%2B1%29+%2B+a%2F%28x-1%29+=+%28-2%29%2F%28x%5E2-1%29\"$ Add the fractions on the left side.
\n" ); document.write( " $\"%28%28x-1%29%2Ba%28x%2B1%29%29%2F%28x%2B1%29%28x-1%29+=+%28-2%29%2F%28x%5E2-1%29\"$ Simplify the left side.
\n" ); document.write( " $\"%28%28x-1%29%2Ba%28x%2B1%29%29%2F%28x%5E2-1%29+=+%28-2%29%2F%28x%5E2-1%29\"$ Multiply both sides by (x^2-1)
\n" ); document.write( " $\"%28x-1%29%2Ba%28x%2B1%29+=+-2\"$ Subtract (x-1) from both sides.
\n" ); document.write( " $\"a%28x%2B1%29+=+-2-%28x-1%29\"$ Simplify the right side.
\n" ); document.write( " $\"a%28x%2B1%29+=+-%28x%2B1%29\"$ Finally, divide both sides by (x+1)
\n" ); document.write( " $\"a+=+-1\"$ \r
\n" ); document.write( "\n" ); document.write( "Answer: a must = -1\r
\n" ); document.write( "\n" ); document.write( "Check: Substitute a = -1\r
\n" ); document.write( "\n" ); document.write( " $\"1%2F%28x%2B1%29+%2B+%28-1%29%2F%28x-1%29+=+%28-2%29%2F%28x%5E2-1%29\"$ Add the fractions on the left side.
\n" ); document.write( " $\"%28%28x-1%29+-+%28x%2B1%29%29%2F%28x%5E2-1%29+=+%28-2%29%2F%28x%5E2-1%29\"$ Simplify the left side.
\n" ); document.write( " $\"%28-2%29%2F%28x%5E2-1%29+=+%28-2%29%2F%28x%5E2-1%29\"$
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