Answer
$x=9$
Work Step by Step
$\dfrac{2}{x-1}=\dfrac{3}{x+3}$
Multiply the whole equation by $(x-1)(x+3)$:
$(x-1)(x+3)\Big(\dfrac{2}{x-1}=\dfrac{3}{x+3}\Big)$
$2(x+3)=3(x-1)$
$2x+6=3x-3$
Solve for $x$:
$2x-3x=-3-6$
$-x=-9$
$x=9$
The original equation is not undefined for this value of $x$, so the solution is $x=9$
