Question
Answer
$$\dfrac{\dfrac{\dfrac{1}{x^3}}{5}}{x^2}=\dfrac{1}{5x^5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{\frac{1}{x^3}}{5}}{x^2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\frac{1}{5x^3}}{x^2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1}{5x^5}\end{aligned} $$ | |
| ① | Divide $ \dfrac{1}{x^3} $ by $ 5 $ to get $ \dfrac{ 1 }{ 5x^3 } $. 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. $$ \begin{aligned} \frac{ \frac{1}{x^3} }{5} & \xlongequal{\text{Step 1}} \frac{1}{x^3} \cdot \frac{\color{blue}{1}}{\color{blue}{5}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot 1 }{ x^3 \cdot 5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 1 }{ 5x^3 } \end{aligned} $$ |
| ② | Divide $ \dfrac{1}{5x^3} $ by $ x^2 $ to get $ \dfrac{ 1 }{ 5x^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. $$ \begin{aligned} \frac{ \frac{1}{5x^3} }{x^2} & \xlongequal{\text{Step 1}} \frac{1}{5x^3} \cdot \frac{\color{blue}{1}}{\color{blue}{x^2}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot 1 }{ 5x^3 \cdot x^2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 1 }{ 5x^5 } \end{aligned} $$ |
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Simplify Rational Expressions