I'd suggest you begin by subtracting 4 / (x-4) from both sides. Doing that would leave you with 1 / (x-4) - 2 / (x+2) = 0.
LCD is (x-4)(x+2). Mult. all three terms by (x-4)(x+2). The resulting equation is
x+2 - 2(x-4) = 0. Then x+2 = 2x - 8 => x = 10
Subst. 10 for x in the original equation to verify that 10 is indeed a solution.
