Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{x^2}{\frac{4}{5}-\frac{4}{x}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{x^2}{\frac{4x-20}{5x}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{5x^3}{4x-20}\end{aligned} $$ | |
| ① | Subtract $ \dfrac{4}{x} $ from $ \dfrac{4}{5} $ to get $ \dfrac{ \color{purple}{ 4x-20 } }{ 5x }$. To subtract raitonal expressions, both fractions must have the same denominator. |
| ② | Divide $x^2$ by $ \dfrac{4x-20}{5x} $ to get $ \dfrac{ 5x^3 }{ 4x-20 } $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Write $ x^2 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 3: Multiply numerators and denominators. Step 4: Simplify numerator and denominator. $$ \begin{aligned} \frac{x^2}{ \frac{\color{blue}{4x-20}}{\color{blue}{5x}} } & \xlongequal{\text{Step 1}} x^2 \cdot \frac{\color{blue}{5x}}{\color{blue}{4x-20}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{x^2}{\color{red}{1}} \cdot \frac{5x}{4x-20} \xlongequal{\text{Step 3}} \frac{ x^2 \cdot 5x }{ 1 \cdot \left( 4x-20 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ 5x^3 }{ 4x-20 } \end{aligned} $$ |