Answer
$x=4$ or $x=-2$
Work Step by Step
$\frac{2x}{x^2+6x+8}=\frac{x}{x+4}-\frac{2}{x+2}$
Multiply the equation by the least common multiplier $(x+4)(x+2)$
$\frac{2x}{x^2+6x+8}⋅(x+4)(x+2)=\frac{x}{x+4}⋅(x+4)(x+2)-\frac{2}{x+2}⋅(x+4)(x+2)$
$2x = x(x+2) - 2(x+4)$
$2x = x^2+2x - 2x-8$
$2x = x^2-8$
$x^2-2x-8$
Use the quadratic formula: $x = \frac{-b±\sqrt{b^2-4ac}}{2a}$
$a=1$, $b=-2$, $c=-8$
$x = \frac{-(-2)±\sqrt{(-2)^2-(4⋅1⋅-8)}}{(2⋅1)}$
$x = \frac{2±\sqrt{4-(-32)}}{2}$
$x = \frac{2±\sqrt{36}}{2}$
$x = \frac{2±6}{2}$
$x = \frac{2+6}{2}$ or $x = \frac{2-6}{2}$
$x=4$ or $x=-2$
