Answer
$$\frac{7v^3+49v^2}{v^2+15v+56}=\frac{7v^2}{v+8}$$
Explanation
| $$ \begin{aligned}\frac{7v^3+49v^2}{v^2+15v+56}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{7v^2}{v+8}\end{aligned} $$ | |
| ① | Simplify $ \dfrac{7v^3+49v^2}{v^2+15v+56} $ to $ \dfrac{7v^2}{v+8} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{v+7}$. $$ \begin{aligned} \frac{7v^3+49v^2}{v^2+15v+56} & =\frac{ 7v^2 \cdot \color{blue}{ \left( v+7 \right) }}{ \left( v+8 \right) \cdot \color{blue}{ \left( v+7 \right) }} = \\[1ex] &= \frac{7v^2}{v+8} \end{aligned} $$ |
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Simplify Rational Expressions