Answer
$x = -7$
Work Step by Step
$\frac{6}{x+2} + 4 = \frac{4x}{x-3}$
$6 + 4(x+2) = \frac{4x(x+2)}{x-3}$
$6 + 4x + 8 = \frac{4x^{2}+8x}{x-3}$
$6(x-3) + 4x(x-3) + 8(x-3) = 4x^{2} + 8x$
$6x - 18 + 4x^{2} - 12x + 8x - 24 = 4x^{2} + 8x$
$4x^{2} - 6x + 8x - 42 = 4x^{2} + 8x$
$-6x - 42 = 0$
$-6x = 42$
$x = -7$
Check:
$\frac{6}{x+2} + 4 \overset{?}{=} \frac{4x}{x-3}$
$\frac{6}{(-7)+2} + 4 \overset{?}{=} \frac{4(-7)}{-7-3}$
$\frac{6}{-5} + 4 \overset{?}{=} \frac{-28}{-10}$
$-\frac{6}{5} + 4 \overset{?}{=} \frac{28}{10}$
$\frac{14}{5} \overset{?}{=} \frac{28}{10}$
$\frac{14}{5} = \frac{14}{5}$
