Answer
$x=(-2-\sqrt {11})$, $x=(-2+\sqrt {11})$
Work Step by Step
$4/(x+2) + (2x)/(x-2) = 6/(x^2-4)$
$4/(x+2) + (2x)/(x-2) = 6/(x-2)(x+2)$
$4*(x+2)/(x+2) + (2x)*(x+2)/(x-2) = 6*(x+2)/(x-2)(x+2)$
$4 + (2x)*(x+2)/(x-2) = 6/(x-2)$
$4*(x-2) + (2x)*(x+2)*(x-2)/(x-2) = 6*(x-2)/(x-2)$
$4*(x-2) + (2x)*(x+2) = 6$
$4x-8+2x^2+4x=6$
$2x^2+8x-8=6$
$2x^2+8x-8-6=6-6$
$2x^2+8x-14=0$
$a=2$, $b=8$, $c=-14$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-8±\sqrt {8^2-4*2*-14})/2*2$
$x=(-8±\sqrt {64+4*2*14})/4$
$x=(-8±\sqrt {64+112})/4$
$x=(-8±\sqrt {176})/4$
$x=(-8±\sqrt {11*16})/4$
$x=(-8±4\sqrt {11})/4$
$x=(-2±\sqrt {11})$
$x=(-2+\sqrt {11})$
$x=(-2-\sqrt {11})$
