SOLUTION: In order for the identity {{{1/(x+1)+a/(x-1)=(-2)/(x^2-1)}}} to hold for all x, a must equal ?

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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 ?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Here's one approach:
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.
%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.
%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)
%28x-1%29%2Ba%28x%2B1%29+=+-2 Subtract (x-1) from both sides.
a%28x%2B1%29+=+-2-%28x-1%29 Simplify the right side.
a%28x%2B1%29+=+-%28x%2B1%29 Finally, divide both sides by (x+1)
a+=+-1
Answer: a must = -1
Check: Substitute a = -1
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.
%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.
%28-2%29%2F%28x%5E2-1%29+=+%28-2%29%2F%28x%5E2-1%29