Answer
$x=0$
Work Step by Step
We solve the equation:
$\displaystyle \frac{x+1}{x-1}=\frac{2x-1}{2x+1}$
First we cross-multiply:
$(x+1)(2x+1)=(2x-1)(x-1)$
Next we distribute:
$2x^{2}+3x+1=2x^{2}-3x+1$
And simplify:
$2x^{2}-2x^{2}+3x+3x+1-1=0$
$6x=0$
$x=0$
