Answer
$$\frac{-2x^2+11x+6}{-x^2+4x+12}=\frac{2x+1}{x+2}$$
Explanation
| $$ \begin{aligned}\frac{-2x^2+11x+6}{-x^2+4x+12}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{2x+1}{x+2}\end{aligned} $$ | |
| ① | Simplify $ \dfrac{-2x^2+11x+6}{-x^2+4x+12} $ to $ \dfrac{2x+1}{x+2} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{x-6}$. $$ \begin{aligned} \frac{-2x^2+11x+6}{-x^2+4x+12} & =\frac{ \left( -2x-1 \right) \cdot \color{blue}{ \left( x-6 \right) }}{ \left( -x-2 \right) \cdot \color{blue}{ \left( x-6 \right) }} = \\[1ex] &= \frac{2x+1}{x+2} \end{aligned} $$ |
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Simplify Rational Expressions