Chapter 6 - Section 6.6 - Rational Equations and Problem Solving - Exercise Set - Page 389: 61

$x=-5$

By cross-multiplication and using the properties of equality, the solution to the given equation, $ \dfrac{x}{5}=\dfrac{x+2}{3} ,$ is \begin{array}{l} 3x=5(x+2) \\\\ 3x=5x+10 \\\\ 3x-5x=10 \\\\ -2x=10 \\\\ x=\dfrac{10}{-2} \\\\ x=-5 .\end{array}