Question
Answer
$$\dfrac{2s^2+16s+30}{s^2-4s-21}=\dfrac{2s+10}{s-7}$$
Explanation
| $$ \begin{aligned}\frac{2s^2+16s+30}{s^2-4s-21}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2s+10}{s-7}\end{aligned} $$ | |
| ① | Simplify $ \dfrac{2s^2+16s+30}{s^2-4s-21} $ to $ \dfrac{2s+10}{s-7} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{s+3}$. $$ \begin{aligned} \frac{2s^2+16s+30}{s^2-4s-21} & =\frac{ \left( 2s+10 \right) \cdot \color{blue}{ \left( s+3 \right) }}{ \left( s-7 \right) \cdot \color{blue}{ \left( s+3 \right) }} = \\[1ex] &= \frac{2s+10}{s-7} \end{aligned} $$ |
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Simplify Rational Expressions