## Algebra: A Combined Approach (4th Edition)

$x=9$
$\dfrac{2}{x-1}=\dfrac{3}{x+3}$ 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 $x=9$