Question
Answer
$$\dfrac{2x^2+13x+20}{2x^2+17x+30}=\dfrac{x+4}{x+6}$$
Explanation
| $$ \begin{aligned}\frac{2x^2+13x+20}{2x^2+17x+30}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{x+4}{x+6}\end{aligned} $$ | |
| ① | Simplify $ \dfrac{2x^2+13x+20}{2x^2+17x+30} $ to $ \dfrac{x+4}{x+6} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{2x+5}$. $$ \begin{aligned} \frac{2x^2+13x+20}{2x^2+17x+30} & =\frac{ \left( x+4 \right) \cdot \color{blue}{ \left( 2x+5 \right) }}{ \left( x+6 \right) \cdot \color{blue}{ \left( 2x+5 \right) }} = \\[1ex] &= \frac{x+4}{x+6} \end{aligned} $$ |
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