Answer
$$\frac{8}{\frac{4}{9}+\frac{16}{9}}=\frac{18}{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{8}{\frac{4}{9}+\frac{16}{9}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{8}{\frac{20}{9}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{18}{5}\end{aligned} $$ | |
| ① | Combine like terms |
| ② | Divide $8$ by $ \dfrac{20}{9} $ to get $ \dfrac{18}{5} $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Write $ 8 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 3: Multiply numerators and denominators. Step 4: Cancel down by $ \color{blue}{4} $ $$ \begin{aligned} \frac{8}{ \frac{\color{blue}{20}}{\color{blue}{9}} } & \xlongequal{\text{Step 1}} 8 \cdot \frac{\color{blue}{9}}{\color{blue}{20}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{8}{\color{red}{1}} \cdot \frac{9}{20} \xlongequal{\text{Step 3}} \frac{72 : \color{blue}{4}}{20 : \color{blue}{4}}= \frac{18}{5} \end{aligned} $$ |
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Simplify Rational Expressions