Answer
$x=\frac{-a+1}{a^{2}-a-1}$
Work Step by Step
$a^{2}x+(a-1)=(a+1)x$
We move $x$ terms to one side:
$a^{2}x-(a+1)x=-(a-1)$
Then we factor out $x$:
$(a^{2}-(a+1))x=-a+1$
And simplify:
$(a^{2}-a-1)x=-a+1$
Finally, we solve for $x$:
$x=\frac{-a+1}{a^{2}-a-1}$
