Question
Answer
$$\dfrac{\dfrac{\dfrac{27x-27}{5}}{9x-9}}{10}=\dfrac{3}{50}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{\frac{27x-27}{5}}{9x-9}}{10}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\frac{3}{5}}{10} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{3}{50}\end{aligned} $$ | |
| ① | Divide $ \dfrac{27x-27}{5} $ by $ 9x-9 $ to get $ \dfrac{ 3 }{ 5 } $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Factor numerators and denominators. Step 3: Cancel common factors. Step 4: Multiply numerators and denominators. $$ \begin{aligned} \frac{ \frac{27x-27}{5} }{9x-9} & \xlongequal{\text{Step 1}} \frac{27x-27}{5} \cdot \frac{\color{blue}{1}}{\color{blue}{9x-9}} \xlongequal{\text{Step 2}} \frac{ 3 \cdot \color{blue}{ \left( 9x-9 \right) } }{ 5 } \cdot \frac{ 1 }{ 1 \cdot \color{blue}{ \left( 9x-9 \right) } } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3 }{ 5 } \cdot \frac{ 1 }{ 1 } \xlongequal{\text{Step 4}} \frac{ 3 }{ 5 } \end{aligned} $$ |
| ② | Divide $ \dfrac{3}{5} $ by $ 10 $ to get $ \dfrac{3}{50} $. To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Multiply numerators and denominators. $$ \begin{aligned} \frac{ \frac{3}{5} }{10} = \frac{3}{5} \cdot \frac{\color{blue}{1}}{\color{blue}{10}} = \frac{3}{50} \end{aligned} $$ |
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Simplify Rational Expressions