SOLUTION: For what value(s) of x is the reciprocal of x+1 equal to x-1?

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Question 34215: For what value(s) of x is the reciprocal of x+1 equal to x-1?
Found 2 solutions by dimndskier, stanbon:
Answer by dimndskier(8) About Me  (Show Source):
You can put this solution on YOUR website!
Here is an example problem instead of THE answer so you can LEARN how to do this.

0) +5%2F%28x%2B2%29+=+%28x-2%29+
1) +%285%2F%28x%2B2%29%29%2A%28x%2B2%29+=+%28x-2%29%2A%28x%2B2%29+
2) +5+=+%28x-2%29%2A%28x%2B2%29+
3) +x%5E2+-+4+=+5+
4) +x%5E2+-4+-5+=+5+-5+=+0+
5) +x%5E2+-+9+=+0+
6) +sqrt%28x%5E2%29+=+sqrt%289%29+
7) +abs+%28x%29+=+3+ , so x =+3 or x =-3
Check x= +3:
a) +5%2F%283%2B2%29+=+%283-2%29+
b) +5%2F5+=+1+
c) +1+=+1+
Check x= -3:
a) +5%2F%28-3%2B2%29+=+%28-3-2%29+
b) +5%2F%28-5%29+=+-1+
c) +-1+=+-1+

Answer by stanbon(48558) About Me  (Show Source):
You can put this solution on YOUR website!
1/(x+1)= x-1
Multiply both sides by x+1 to get:
1=x^2-1
x^2=2
x=+sqrt2 or z=-sqrt2
Cheers,
Stan H.