Answer
$\dfrac{3x}{x^{2}+9x+14}-\dfrac{6x}{x^{2}+4x-21}=-\dfrac{3x}{(x+2)(x-3)}$
Work Step by Step
$\dfrac{3x}{x^{2}+9x+14}-\dfrac{6x}{x^{2}+4x-21}$
Factor both denominators:
$\dfrac{3x}{(x+7)(x+2)}-\dfrac{6x}{(x+7)(x-3)}=...$
Evaluate the substraction:
$...=\dfrac{3x(x-3)-6x(x+2)}{(x+7)(x+2)(x-3)}=\dfrac{3x^{2}-9x-6x^{2}-12x}{(x+7)(x+2)(x-3)}=...$
$...=\dfrac{-3x^{2}-21x}{(x+7)(x+2)(x-3)}=...$
Take out common factor $-3x$ from the numerator and simplify:
$...=\dfrac{-3x(x+7)}{(x+7)(x+2)(x-3)}=-\dfrac{3x}{(x+2)(x-3)}$
