Question
Answer
$$\dfrac{8x^3-27}{2x^2+7x-15}=\dfrac{4x^2+6x+9}{x+5}$$
Explanation
| $$ \begin{aligned}\frac{8x^3-27}{2x^2+7x-15}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{4x^2+6x+9}{x+5}\end{aligned} $$ | |
| ① | Simplify $ \dfrac{8x^3-27}{2x^2+7x-15} $ to $ \dfrac{4x^2+6x+9}{x+5} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{2x-3}$. $$ \begin{aligned} \frac{8x^3-27}{2x^2+7x-15} & =\frac{ \left( 4x^2+6x+9 \right) \cdot \color{blue}{ \left( 2x-3 \right) }}{ \left( x+5 \right) \cdot \color{blue}{ \left( 2x-3 \right) }} = \\[1ex] &= \frac{4x^2+6x+9}{x+5} \end{aligned} $$ |
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Simplify Rational Expressions