## Precalculus: Mathematics for Calculus, 7th Edition

$\dfrac{2x(x+6)^{4}-x^{2}(4)(x+6)^{3}}{(x+6)^{8}}=\dfrac{2x(6-x)}{(x+6)^{5}}$
$\dfrac{2x(x+6)^{4}-x^{2}(4)(x+6)^{3}}{(x+6)^{8}}$ Take out common factor $2x(x+6)^{3}$ from the numerator and simplify: $\dfrac{2x(x+6)^{4}-x^{2}(4)(x+6)^{3}}{(x+6)^{8}}=\dfrac{2x(x+6)^{3}[(x+6)-2x]}{(x+6)^{8}}=...$ $...=\dfrac{2x(x+6)^{3}(-x+6)}{(x+6)^{8}}=\dfrac{2x(6-x)}{(x+6)^{5}}$