Answer
$x=\frac{-9±\sqrt {201}}{6}$
Work Step by Step
$\frac {2x}{x-2} + \frac{x}{x+3} = \frac{-5}{x+3}$
$(x-2)(x+3)*\frac {2x}{x-2} + (x-2)(x+3)*\frac{x}{x+3} = (x-2)(x+3)*\frac{-5}{x+3}$
$(x+3)(2x)+(x-2)(x)=(x-2)(-5)$
$2x^2+6x+x^2-2x=-5x+10$
$3x^2+4x=-5x+10$
$3x^2+9x-10=0$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-9±\sqrt {9^2-4*3*-10})/2*3$
$x=(-9±\sqrt {81+120})/6$
$x=(-9±\sqrt {201})/6$
Neither answer for $x$ would make the denominators negative, so both answers are valid.
