solve this rational Equation x-1 over x+2 + 4x over 2x^2-2x-12 = 2

Question

this is for algebra

Answer 1

(x-1)/(x+2)+4x/(2x²-2x-12)=2,

(x-1)/(x+2)+2x/(x²-x-6)=2,

(x-1)/(x+2)+2x/((x-3)(x+2))=2, multiply through by (x-3)(x+2):

(x-1)(x-3)+2x=2(x-3)(x+2),

x²-4x+3+2x=2x²-2x-12,

x²-2x+3=2x²-2x-12,

3+12=2x²-2x-x²+2x,

15=x², x²=15, x=√15 or -√15.