Question
Answer
$$\dfrac{2x^3+8x^2-15x-60}{x^3+4x^2+3x+12}=\dfrac{2x^2-15}{x^2+3}$$
Explanation
| $$ \begin{aligned}\frac{2x^3+8x^2-15x-60}{x^3+4x^2+3x+12}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2x^2-15}{x^2+3}\end{aligned} $$ | |
| ① | Simplify $ \dfrac{2x^3+8x^2-15x-60}{x^3+4x^2+3x+12} $ to $ \dfrac{2x^2-15}{x^2+3} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{x+4}$. $$ \begin{aligned} \frac{2x^3+8x^2-15x-60}{x^3+4x^2+3x+12} & =\frac{ \left( 2x^2-15 \right) \cdot \color{blue}{ \left( x+4 \right) }}{ \left( x^2+3 \right) \cdot \color{blue}{ \left( x+4 \right) }} = \\[1ex] &= \frac{2x^2-15}{x^2+3} \end{aligned} $$ |
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