Question
Answer
$$\dfrac{v^2+7v+10}{2v^2+15v+22}=\dfrac{v+5}{2v+11}$$
Explanation
| $$ \begin{aligned}\frac{v^2+7v+10}{2v^2+15v+22}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{v+5}{2v+11}\end{aligned} $$ | |
| ① | Simplify $ \dfrac{v^2+7v+10}{2v^2+15v+22} $ to $ \dfrac{v+5}{2v+11} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{v+2}$. $$ \begin{aligned} \frac{v^2+7v+10}{2v^2+15v+22} & =\frac{ \left( v+5 \right) \cdot \color{blue}{ \left( v+2 \right) }}{ \left( 2v+11 \right) \cdot \color{blue}{ \left( v+2 \right) }} = \\[1ex] &= \frac{v+5}{2v+11} \end{aligned} $$ |
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