Question
Answer
$$\dfrac{s^2-2s-8}{s^2-9s+20}=\dfrac{s+2}{s-5}$$
Explanation
| $$ \begin{aligned}\frac{s^2-2s-8}{s^2-9s+20}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{s+2}{s-5}\end{aligned} $$ | |
| ① | Simplify $ \dfrac{s^2-2s-8}{s^2-9s+20} $ to $ \dfrac{s+2}{s-5} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{s-4}$. $$ \begin{aligned} \frac{s^2-2s-8}{s^2-9s+20} & =\frac{ \left( s+2 \right) \cdot \color{blue}{ \left( s-4 \right) }}{ \left( s-5 \right) \cdot \color{blue}{ \left( s-4 \right) }} = \\[1ex] &= \frac{s+2}{s-5} \end{aligned} $$ |
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Simplify Rational Expressions