Answer
no solution
Work Step by Step
By cross-multiplication, the given expression, $
\dfrac{x+6}{x-2}=\dfrac{2(x+2)}{x-2}
,$ is equivalent to
\begin{array}{l}\require{cancel}
(x+6)(x-2)=2(x+2)(x-2)
\\\\
x(x)+x(-2)+6(x)+6(-2)=2(x^2-4)
\\\\
x^2-2x+6x-12=2x^2-8
\\\\
(x^2-2x^2)+(-2x+6x)+(-12+8)=0
\\\\
-x^2+4x-4=0
\\\\
x^2-4x+4=0
\\\\
(x-2)^2=0
\\\\
\sqrt{(x-2)^2}=\sqrt{0}
\\\\
x-2=0
\\\\
x=2
.\end{array}
Upon checking, $x=2$ does not satisfy the original equation. Hence, there is $\text{
no solution
.}$
