Answer
$x=\{ 1,7 \}$
Work Step by Step
The factored form of the given equation, $
\dfrac{x^2-20}{x^2-7x+12}=\dfrac{3}{x-3}+\dfrac{5}{x-4}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{x^2-20}{(x-3)(x-4)}=\dfrac{3}{x-3}+\dfrac{5}{x-4}
.\end{array}
Multiplying both sides by the $LCD=
(x-3)(x-4)
,$ then the solution to the given equation is
\begin{array}{l}\require{cancel}
1(x^2-20)=(x-4)(3)+(x-3)(5)
\\\\
x^2-20=3x-12+5x-15
\\\\
x^2-3x-5x-20+12+15=0
\\\\
x^2-8x+7=0
\\\\
(x-7)(x-1)=0
\\\\
x=\{ 1,7 \}
.\end{array}
