## Algebra: A Combined Approach (4th Edition)

$\dfrac{\dfrac{6}{x+2}+4}{\dfrac{8}{x+2}-4}=-\dfrac{2x+7}{2x}$
$\dfrac{\dfrac{6}{x+2}+4}{\dfrac{8}{x+2}-4}$ Evaluate the sum indicated in the numerator and the substraction indicated in the denominator: $\dfrac{\dfrac{6}{x+2}+4}{\dfrac{8}{x+2}-4}=\dfrac{\dfrac{6+4(x+2)}{x+2}}{\dfrac{8-4(x+2)}{x+2}}=\dfrac{\dfrac{6+4x+8}{x+2}}{\dfrac{8-4x-8}{x+2}}=...$ $...=\dfrac{\dfrac{4x+14}{x+2}}{\dfrac{-4x}{x+2}}=...$ Evaluate the division and simplify: $...=\dfrac{4x+14}{x+2}\div\dfrac{-4x}{x+2}=\dfrac{(4x+14)(x+2)}{-4x(x+2)}=...$ $...=\dfrac{4x+14}{-4x}=...$ Take out common factor $2$ from the numerator and simplify one more time: $...=\dfrac{2(2x+7)}{-4x}=-\dfrac{2x+7}{2x}$