Answer
$$\frac{6v^3+42v^2}{2v^2+26v+84}=\frac{3v^2}{v+6}$$
Explanation
| $$ \begin{aligned}\frac{6v^3+42v^2}{2v^2+26v+84}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3v^2}{v+6}\end{aligned} $$ | |
| ① | Simplify $ \dfrac{6v^3+42v^2}{2v^2+26v+84} $ to $ \dfrac{3v^2}{v+6} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{2v+14}$. $$ \begin{aligned} \frac{6v^3+42v^2}{2v^2+26v+84} & =\frac{ 3v^2 \cdot \color{blue}{ \left( 2v+14 \right) }}{ \left( v+6 \right) \cdot \color{blue}{ \left( 2v+14 \right) }} = \\[1ex] &= \frac{3v^2}{v+6} \end{aligned} $$ |
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Simplify Rational Expressions