Question
Answer
$$\dfrac{15m^2-45m+30}{4m^3+4m^2-24m}=\dfrac{15m-15}{4m^2+12m}$$
Explanation
| $$ \begin{aligned}\frac{15m^2-45m+30}{4m^3+4m^2-24m}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{15m-15}{4m^2+12m}\end{aligned} $$ | |
| ① | Simplify $ \dfrac{15m^2-45m+30}{4m^3+4m^2-24m} $ to $ \dfrac{15m-15}{4m^2+12m} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{m-2}$. $$ \begin{aligned} \frac{15m^2-45m+30}{4m^3+4m^2-24m} & =\frac{ \left( 15m-15 \right) \cdot \color{blue}{ \left( m-2 \right) }}{ \left( 4m^2+12m \right) \cdot \color{blue}{ \left( m-2 \right) }} = \\[1ex] &= \frac{15m-15}{4m^2+12m} \end{aligned} $$ |
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