Answer
$$\frac{u^3+13u^2+42u}{u^2+14u+49}=\frac{u^2+6u}{u+7}$$
Explanation
| $$ \begin{aligned}\frac{u^3+13u^2+42u}{u^2+14u+49}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{u^2+6u}{u+7}\end{aligned} $$ | |
| ① | Simplify $ \dfrac{u^3+13u^2+42u}{u^2+14u+49} $ to $ \dfrac{u^2+6u}{u+7} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{u+7}$. $$ \begin{aligned} \frac{u^3+13u^2+42u}{u^2+14u+49} & =\frac{ \left( u^2+6u \right) \cdot \color{blue}{ \left( u+7 \right) }}{ \left( u+7 \right) \cdot \color{blue}{ \left( u+7 \right) }} = \\[1ex] &= \frac{u^2+6u}{u+7} \end{aligned} $$ |
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Simplify Rational Expressions