Chapter 6 - Sections 6.1-6.5 - Integrated Review - Expressions and Equations Containing Rational Expressions - Page 380: 8

$x=8$

By cross-multiplication, the solution to the given equation, $ \dfrac{5}{x-2}=\dfrac{10}{x+4} ,$ is \begin{array}{l} 5(x+4)=10(x-2) \\\\ 5x+20=10x-20 \\\\ 5x-10x=-20-20 \\\\ -5x=-40 \\\\ x=\dfrac{-40}{-5} \\\\ x=8 .\end{array}