-x/(x-3) + 2x/(x+2) (x-1) x (x-2) (x+2)/(x-3)(x-3)

Question

my question is should i multiply first and then do the adding or subtracting through a LCD or should i do the adding first?

Answer 1

If you use some parentheses to properly specify the numerators and denominators, I think you have a typo and meant

-x/(x-3) + 2x/((x+2)(x-1)) * ((x-2)(x+2))/((x-3)(x+3))

As usual, do multiplication before addition. In effect you have

-x + y * z

Do the y*z first, giving you

-x/(x-3) + (2x(x-2)(x+2))/((x+2)(x-1)(x-3)(x+3))

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

Nor you need to get the GCD before you can do the addition. That gives you

(-x(x-1)(x+3) + 2x(x-2))/((x-1)(x-3)(x+3))

(-x^3-x)/((x-1)(x-3)(x+3))

= -(x(x^2+1))/((x-1)(x-3)(x+3))