Question 989440

If the reciprocal of 2x+1 is 2x-1, find x.
<pre>
{{{1/(2x+1)=2x-1}}}

Multiply both sides by (2x+1)

{{{1=(2x-1)(2x+1)}}}

{{{1=4x^2-1}}}

{{{0=4x^2-2}}}

Divide through by 2

{{{0=2x^2-1}}}

{{{1=2x^2}}}

{{{1/2=x^2}}}

{{{"" +- sqrt(1/2) = x}}}

{{{"" +- 1/sqrt(2) = x}}}

Rationalize by multiplying by {{{sqrt(2)/sqrt(2)}}}

{{{"" +- sqrt(2)/2 = x}}}

Edwin</pre>