SOLUTION: If the reciprocal of 2x +1 is 2x-1, find x. Thanks!!

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Question 989440: If the reciprocal of 2x +1 is 2x-1, find x.
Thanks!!
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!

If the reciprocal of 2x+1 is 2x-1, find x.
1%2F%282x%2B1%29=2x-1

Multiply both sides by (2x+1)

1=%282x-1%29%282x%2B1%29

1=4x%5E2-1

0=4x%5E2-2

Divide through by 2

0=2x%5E2-1

1=2x%5E2

1%2F2=x%5E2

%22%22+%2B-+sqrt%281%2F2%29+=+x

%22%22+%2B-+1%2Fsqrt%282%29+=+x

Rationalize by multiplying by sqrt%282%29%2Fsqrt%282%29

%22%22+%2B-+sqrt%282%29%2F2+=+x

Edwin