Question
Answer
$$\dfrac{\dfrac{\dfrac{1}{iwc}}{irwc-w^2lc}}{iwc}=\dfrac{1}{c^3i^3rw^3-c^3i^2lw^4}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{\frac{1}{iwc}}{irwc-w^2lc}}{iwc}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\frac{1}{c^2i^2rw^2-c^2ilw^3}}{iwc} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{1}{c^3i^3rw^3-c^3i^2lw^4}\end{aligned} $$ | |
| ① | Divide $ \dfrac{1}{ciw} $ by $ cirw-clw^2 $ to get $ \dfrac{ 1 }{ c^2i^2rw^2-c^2ilw^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. $$ \begin{aligned} \frac{ \frac{1}{ciw} }{cirw-clw^2} & \xlongequal{\text{Step 1}} \frac{1}{ciw} \cdot \frac{\color{blue}{1}}{\color{blue}{cirw-clw^2}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 1 \cdot 1 }{ ciw \cdot \left( cirw-clw^2 \right) } \xlongequal{\text{Step 3}} \frac{ 1 }{ c^2i^2rw^2-c^2ilw^3 } \end{aligned} $$ |
| ② | Divide $ \dfrac{1}{c^2i^2rw^2-c^2ilw^3} $ by $ ciw $ to get $ \dfrac{ 1 }{ c^3i^3rw^3-c^3i^2lw^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. $$ \begin{aligned} \frac{ \frac{1}{c^2i^2rw^2-c^2ilw^3} }{ciw} & \xlongequal{\text{Step 1}} \frac{1}{c^2i^2rw^2-c^2ilw^3} \cdot \frac{\color{blue}{1}}{\color{blue}{ciw}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 1 \cdot 1 }{ \left( c^2i^2rw^2-c^2ilw^3 \right) \cdot ciw } \xlongequal{\text{Step 3}} \frac{ 1 }{ c^3i^3rw^3-c^3i^2lw^4 } \end{aligned} $$ |
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