Question
Answer
$$\dfrac{-\dfrac{9}{2}+5}{\dfrac{9}{2}-7}=-\dfrac{1}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{-\frac{9}{2}+5}{\frac{9}{2}-7}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\frac{1}{2}}{-\frac{5}{2}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{1}{-5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-\frac{1}{5}\end{aligned} $$ | |
| ① | Combine like terms |
| ② | Combine like terms |
| ③ | Divide $ \dfrac{1}{2} $ by $ \dfrac{-5}{2} $ to get $ \dfrac{1}{-5} $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Cancel $ \color{red}{ 2 } $ in first and second fraction. Step 3: Multiply numerators and denominators. $$ \begin{aligned} \frac{ \frac{1}{2} }{ \frac{\color{blue}{-5}}{\color{blue}{2}} } & \xlongequal{\text{Step 1}} \frac{1}{2} \cdot \frac{\color{blue}{2}}{\color{blue}{-5}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{1}{\color{red}{1}} \cdot \frac{\color{red}{1}}{-5} = \frac{1}{-5} \end{aligned} $$ |
| ④ | Place minus sign in front of the fraction. |
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Simplify Rational Expressions