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