Answer
Solution set = $\{38\}$.
Work Step by Step
First, we exclude those values of x that yield a zero in any of the denominators.
$x\not\in\{-4,-10\}\qquad (*)$
Multiply the equation with the LCD=$(x+10)(x+4)$
$(x+2)(x+4)=(x-3)(x+10)\qquad$ ... simplify (distribute)
$x^{2}+4x+2x+8=x^{2}+10x-3x-30$
$ x^{2}+6x+8=x^{2}+7x-30\qquad$ ... add $-8-x^{2}-7x$
$6x-7x=-30-8$
$-x=-38$
$ x=38\qquad$ ...Checking (*), this is a valid solution
Solution set = $\{38\}$.
