Answer
$x=7$
Work Step by Step
$\dfrac{6}{x+3}-\dfrac{5}{x-2}=\dfrac{-20}{x^{2}+x-6}$
Factor the denominator of the fraction on the right side:
$\dfrac{6}{x+3}-\dfrac{5}{x-2}=\dfrac{-20}{(x+3)(x-2)}$
Multiply the whole fraction by $(x+3)(x-2)$:
$(x+3)(x-2)\Big[\dfrac{6}{x+3}-\dfrac{5}{x-2}=\dfrac{-20}{(x+3)(x-2)}\Big]$
$6(x-2)-5(x+3)=-20$
$6x-12-5x-15=-20$
Take all terms without $x$ to the right side of the equation, simplify and solve for $x$:
$6x-5x=-20+15+12$
$x=7$
