Answer
$x=\left\{ \dfrac{2}{3},5 \right\}$
Work Step by Step
Multiplying both sides by the $LCD=
x(x-2)
,$ the solution/s to the given equation, $
\dfrac{5}{x}+\dfrac{6}{x-2}=3
,$ is/are
\begin{array}{l}\require{cancel}
(x-2)(5)+x(6)=x(x-2)(3)
\\\\
5x-10+6x=3x^2-6x
\\\\
0=3x^2+(-6x-6x-5x)+10
\\\\
3x^2-17x+10=0
\\\\
(3x-2)(x-5)=0
\\\\
x=\left\{ \dfrac{2}{3},5 \right\}
.\end{array}
