Answer
$$\frac{x-4}{4-x}=-1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{x-4}{4-x}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1}{-1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-\frac{1}{1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-1\end{aligned} $$ | |
| ① | Simplify $ \dfrac{x-4}{4-x} $ to $ \dfrac{1}{-1} $. Factor both the denominator and the numerator, then cancel the common factor. $\color{blue}{x-4}$. $$ \begin{aligned} \frac{x-4}{4-x} & =\frac{ 1 \cdot \color{blue}{ \left( x-4 \right) }}{ \left( -1 \right) \cdot \color{blue}{ \left( x-4 \right) }} = \\[1ex] &= \frac{1}{-1} \end{aligned} $$ |
| ② | Place minus sign in front of the fraction. |
| ③ | Remove 1 from denominator. |
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Simplify Rational Expressions