Answer
$\dfrac{4}{3x^{2}+8x-3}+\dfrac{2}{3x^{2}-7x+2}=\dfrac{2}{(x+3)(x-2)}$
Work Step by Step
$\dfrac{4}{3x^{2}+8x-3}+\dfrac{2}{3x^{2}-7x+2}$
Factor both denominators:
$\dfrac{4}{(x+3)(3x-1)}+\dfrac{2}{(3x-1)(x-2)}=...$
Evaluate the sum:
$...=\dfrac{4(x-2)+2(x+3)}{(x+3)(x-2)(3x-1)}=\dfrac{4x-8+2x+6}{(x+3)(x-2)(3x-1)}=...$
$...=\dfrac{6x-2}{(x+3)(x-2)(3x-1)}=...$
Take out common factor $2$ from the numerator and simplify:
$...=\dfrac{2(3x-1)}{(x+3)(x-2)(3x-1)}=\dfrac{2}{(x+3)(x-2)}$
