Question
Answer
$$\dfrac{7x^2+56x+105}{9x^2+72x+135}=\dfrac{7}{9}$$
Explanation
| $$ \begin{aligned}\frac{7x^2+56x+105}{9x^2+72x+135}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{7}{9}\end{aligned} $$ | |
| ① | Simplify $ \dfrac{7x^2+56x+105}{9x^2+72x+135} $ to $ \dfrac{7}{9} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{x^2+8x+15}$. $$ \begin{aligned} \frac{7x^2+56x+105}{9x^2+72x+135} & =\frac{ 7 \cdot \color{blue}{ \left( x^2+8x+15 \right) }}{ 9 \cdot \color{blue}{ \left( x^2+8x+15 \right) }} = \\[1ex] &= \frac{7}{9} \end{aligned} $$ |
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Simplify Rational Expressions