Answer
$x=4$
Work Step by Step
$x-\frac{6}{x+3} = \frac{2x}{x+3}+2$
$\frac{x(x+3)}{x+3}-\frac{6}{x+3} = \frac{2x}{x+3}+\frac{2(x+3)}{x+3}$
$x(x+3)-6 = 2x+2(x+3)$
$x^2+3x-6=2x+2x+6$
$x^2+3x-6=4x+6$
$x^2-x-12=0$
$(x-4)(x+3)=0$
$x-4=0$
$x=4$
$x+3=0$
$x=-3$ (This causes the denominator to be zero, so this is not a valid answer.)
$x=4$
$x-\frac{6}{x+3} = \frac{2x}{x+3}+2$
$4-\frac{6}{4+3} = \frac{2*4}{4+3}+2$
$4-\frac{6}{7} = \frac{8}{7}+2$
$28/7-6/7 = 8/7 + 14/7$
$22/7 = 22/7$
