Question
Answer
$$\dfrac{\dfrac{\dfrac{a}{2}}{a^2}}{4}=\dfrac{a}{8a^2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{\frac{a}{2}}{a^2}}{4}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\frac{a}{2a^2}}{4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{a}{8a^2}\end{aligned} $$ | |
| ① | Divide $ \dfrac{a}{2} $ by $ a^2 $ to get $ \dfrac{ a }{ 2a^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. $$ \begin{aligned} \frac{ \frac{a}{2} }{a^2} & \xlongequal{\text{Step 1}} \frac{a}{2} \cdot \frac{\color{blue}{1}}{\color{blue}{a^2}} \xlongequal{\text{Step 2}} \frac{ a \cdot 1 }{ 2 \cdot a^2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ a }{ 2a^2 } \end{aligned} $$ |
| ② | Divide $ \dfrac{a}{2a^2} $ by $ 4 $ to get $ \dfrac{ a }{ 8a^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. $$ \begin{aligned} \frac{ \frac{a}{2a^2} }{4} & \xlongequal{\text{Step 1}} \frac{a}{2a^2} \cdot \frac{\color{blue}{1}}{\color{blue}{4}} \xlongequal{\text{Step 2}} \frac{ a \cdot 1 }{ 2a^2 \cdot 4 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ a }{ 8a^2 } \end{aligned} $$ |
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Simplify Rational Expressions