$$12\cdot\dfrac{\dfrac{\dfrac{x}{y^2}}{4}}{y^3}=\dfrac{12x}{4y^5}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}12 \cdot \frac{\frac{\frac{x}{y^2}}{4}}{y^3}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}12 \cdot \frac{\frac{x}{4y^2}}{y^3} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}12 \cdot \frac{x}{4y^5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{12x}{4y^5}\end{aligned} $$ | |
| ① | Divide $ \dfrac{x}{y^2} $ by $ 4 $ to get $ \dfrac{ x }{ 4y^2 } $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{ \frac{x}{y^2} }{4} & \xlongequal{\text{Step 1}} \frac{x}{y^2} \cdot \frac{\color{blue}{1}}{\color{blue}{4}} \xlongequal{\text{Step 2}} \frac{ x \cdot 1 }{ y^2 \cdot 4 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x }{ 4y^2 } \end{aligned} $$ |
| ② | Divide $ \dfrac{x}{4y^2} $ by $ y^3 $ to get $ \dfrac{ x }{ 4y^5 } $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{ \frac{x}{4y^2} }{y^3} & \xlongequal{\text{Step 1}} \frac{x}{4y^2} \cdot \frac{\color{blue}{1}}{\color{blue}{y^3}} \xlongequal{\text{Step 2}} \frac{ x \cdot 1 }{ 4y^2 \cdot y^3 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x }{ 4y^5 } \end{aligned} $$ |
| ③ | Multiply $12$ by $ \dfrac{x}{4y^5} $ to get $ \dfrac{ 12x }{ 4y^5 } $. Step 1: Write $ 12 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 12 \cdot \frac{x}{4y^5} & \xlongequal{\text{Step 1}} \frac{12}{\color{red}{1}} \cdot \frac{x}{4y^5} \xlongequal{\text{Step 2}} \frac{ 12 \cdot x }{ 1 \cdot 4y^5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 12x }{ 4y^5 } \end{aligned} $$ |