Question
Answer
$$\dfrac{-27x^3-9x^2+9x+27}{x-1}=-27x^2-36x-27$$
Explanation
| $$ \begin{aligned}\frac{-27x^3-9x^2+9x+27}{x-1}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-27x^2-36x-27\end{aligned} $$ | |
| ① | Simplify $ \dfrac{-27x^3-9x^2+9x+27}{x-1} $ to $ -27x^2-36x-27$. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{x-1}$. $$ \begin{aligned} \frac{-27x^3-9x^2+9x+27}{x-1} & =\frac{ \left( -27x^2-36x-27 \right) \cdot \color{blue}{ \left( x-1 \right) }}{ 1 \cdot \color{blue}{ \left( x-1 \right) }} = \\[1ex] &= \frac{-27x^2-36x-27}{1} =-27x^2-36x-27 \end{aligned} $$ |
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