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