Question
Answer
$$\dfrac{a^3+27}{2a^2-6a+18}=\dfrac{a+3}{2}$$
Explanation
| $$ \begin{aligned}\frac{a^3+27}{2a^2-6a+18}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{a+3}{2}\end{aligned} $$ | |
| ① | Simplify $ \dfrac{a^3+27}{2a^2-6a+18} $ to $ \dfrac{a+3}{2} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{a^2-3a+9}$. $$ \begin{aligned} \frac{a^3+27}{2a^2-6a+18} & =\frac{ \left( a+3 \right) \cdot \color{blue}{ \left( a^2-3a+9 \right) }}{ 2 \cdot \color{blue}{ \left( a^2-3a+9 \right) }} = \\[1ex] &= \frac{a+3}{2} \end{aligned} $$ |
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Simplify Rational Expressions