Question

3x+6/x^2-x-6+2x/x^2+x-12

Answer 1

$\dfrac{3x+6}{x^2-x-6} + \dfrac{2x}{x^2+x-12}$

$= \dfrac{3(x+2)}{(x + 2)(x - 3)} + \dfrac{2x}{ (x - 3)(x + 4)}$

$= \dfrac{3}{(x - 3)} + \dfrac{2x}{ (x -3)(x + 4)}$

$= \dfrac{3(x+4)}{(x - 3)(x + 4)} + \dfrac{2x}{ (x -3 )(x + 4)}$

$= \dfrac{3(x+4) + 2x }{(x - 3)(x + 4)}$

$= \dfrac{3x+12 + 2x }{(x - 3)(x + 4)}$

$= \dfrac{5x+12}{(x - 3)(x + 4)}$