Answer
$x=-31$
Work Step by Step
Write the denominators in factored form:
$\dfrac{5}{x+3}-\dfrac{6}{x-2}=\dfrac{3}{(x+3)(x-2)}$
Multiply $(x+3)(x-2)$ to both sides of the equation to obtain:
$\require{cancel}
(x+3)(x-2)\left[\dfrac{5}{x+3}-\dfrac{6}{x-2}\right]=(x+3)(x-2)\left[\dfrac{3}{(x+3)(x-2)}\right]$
$\require{cancel}
\\\cancel{(x+3)}(x-2)\left[\dfrac{5}{\cancel{x+3}}\right]-(x+3)\cancel{(x-2)}\left[\dfrac{6}{\cancel{x-2}}\right]=\cancel{(x+3)(x-2)}\left[\dfrac{3}{\cancel{(x+3)(x-2)}}\right]$
$5(x-2)-6(x+3)=3
\\5(x)-5(2)-6(x)-6(3)=3
\\5x-10-6x-18=3
\\-x-28=3
\\-x=3+28
\\-x=31
\\-1(-x)=-1(31)
\\x=-31$
