Answer
$x = \frac{1-a}{a^2-a-1}$
Work Step by Step
$Solve$ $the$ $equation$ $for$ $the$ $indicated$ $variable:$
$a^2x + (a-1) = (a+1)x;$ $for$ $x$
Solve for $x$
Subtract $(a+1)x$ from both sides
$a^2x + (a-1) - (a+1)x$ = $(a+1)x - (a+1)x$
Simplify
$a^2x + (a-1) - (a+1)x = 0$
Subtract $(a-1)$ from both sides
$a^2x + (a-1) - (a+1)x - (a-1)$ = $0 - (a-1)$
Simplify
$a^2x - (a+1)x = -(a-1)$
Factor out $x$ from $a^2x - (a+1)x$
$x(a^2 - (a+1)) = -(a-1)$
$x(a^2 - a - 1) = 1-a$
Divide both sides by $a^2 -a -1$
$\frac{x(a^2 - a - 1)}{a^2 - a - 1} = \frac{1-a}{a^2-a-1}$
Simplify
$x = \frac{1-a}{a^2-a-1}$
