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