Chapter 6 - Test - Page 406: 22

$x=8$

Multiplying both sides by the $LCD= x-4 ,$ then the solution to the given equation, $ \dfrac{x}{x-4}=3-\dfrac{4}{x-4} ,$ is \begin{array}{l}\require{cancel} 1(x)=(x-4)(3)-1(4) \\\\ x=3x-12-4 \\\\ x-3x=-12-4 \\\\ -2x=-16 \\\\ x=\dfrac{-16}{-2} \\\\ x=8 .\end{array}