Question
Answer
$$\dfrac{\dfrac{\dfrac{3}{5x^4}}{x-3}}{2x}=\dfrac{3}{10x^6-30x^5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{\frac{3}{5x^4}}{x-3}}{2x}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\frac{3}{5x^5-15x^4}}{2x} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{3}{10x^6-30x^5}\end{aligned} $$ | |
| ① | Divide $ \dfrac{3}{5x^4} $ by $ x-3 $ to get $ \dfrac{ 3 }{ 5x^5-15x^4 } $. 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. $$ \begin{aligned} \frac{ \frac{3}{5x^4} }{x-3} & \xlongequal{\text{Step 1}} \frac{3}{5x^4} \cdot \frac{\color{blue}{1}}{\color{blue}{x-3}} \xlongequal{\text{Step 2}} \frac{ 3 \cdot 1 }{ 5x^4 \cdot \left( x-3 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3 }{ 5x^5-15x^4 } \end{aligned} $$ |
| ② | Divide $ \dfrac{3}{5x^5-15x^4} $ by $ 2x $ to get $ \dfrac{ 3 }{ 10x^6-30x^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. $$ \begin{aligned} \frac{ \frac{3}{5x^5-15x^4} }{2x} & \xlongequal{\text{Step 1}} \frac{3}{5x^5-15x^4} \cdot \frac{\color{blue}{1}}{\color{blue}{2x}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 3 \cdot 1 }{ \left( 5x^5-15x^4 \right) \cdot 2x } \xlongequal{\text{Step 3}} \frac{ 3 }{ 10x^6-30x^5 } \end{aligned} $$ |
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