Question
Answer
$$\dfrac{\dfrac{\dfrac{7}{6x^3-2x^2}}{5}}{2x^2}=\dfrac{7}{60x^5-20x^4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{\frac{7}{6x^3-2x^2}}{5}}{2x^2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\frac{7}{30x^3-10x^2}}{2x^2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{7}{60x^5-20x^4}\end{aligned} $$ | |
| ① | Divide $ \dfrac{7}{6x^3-2x^2} $ by $ 5 $ to get $ \dfrac{ 7 }{ 30x^3-10x^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. $$ \begin{aligned} \frac{ \frac{7}{6x^3-2x^2} }{5} & \xlongequal{\text{Step 1}} \frac{7}{6x^3-2x^2} \cdot \frac{\color{blue}{1}}{\color{blue}{5}} \xlongequal{\text{Step 2}} \frac{ 7 \cdot 1 }{ \left( 6x^3-2x^2 \right) \cdot 5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 7 }{ 30x^3-10x^2 } \end{aligned} $$ |
| ② | Divide $ \dfrac{7}{30x^3-10x^2} $ by $ 2x^2 $ to get $ \dfrac{ 7 }{ 60x^5-20x^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. $$ \begin{aligned} \frac{ \frac{7}{30x^3-10x^2} }{2x^2} & \xlongequal{\text{Step 1}} \frac{7}{30x^3-10x^2} \cdot \frac{\color{blue}{1}}{\color{blue}{2x^2}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 7 \cdot 1 }{ \left( 30x^3-10x^2 \right) \cdot 2x^2 } \xlongequal{\text{Step 3}} \frac{ 7 }{ 60x^5-20x^4 } \end{aligned} $$ |
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Simplify Rational Expressions