$$\dfrac{24u^3-12\dfrac{u^2}{3}u^2}{2x+5}=\dfrac{-4u^4+24u^3}{2x+5}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{24u^3-12\frac{u^2}{3}u^2}{2x+5}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{24u^3-\frac{12u^2}{3}u^2}{2x+5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{24u^3-\frac{12u^4}{3}}{2x+5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{\frac{-12u^4+72u^3}{3}}{2x+5} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{-12u^4+72u^3}{6x+15} \xlongequal{ } \\[1 em] & \xlongequal{ }\frac{-4u^4+24u^3}{2x+5}\end{aligned} $$ | |
| ① | Multiply $12$ by $ \dfrac{u^2}{3} $ to get $ \dfrac{ 12u^2 }{ 3 } $. Step 1: Write $ 12 $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} 12 \cdot \frac{u^2}{3} & \xlongequal{\text{Step 1}} \frac{12}{\color{red}{1}} \cdot \frac{u^2}{3} \xlongequal{\text{Step 2}} \frac{ 12 \cdot u^2 }{ 1 \cdot 3 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 12u^2 }{ 3 } \end{aligned} $$ |
| ② | Multiply $ \dfrac{12u^2}{3} $ by $ u^2 $ to get $ \dfrac{ 12u^4 }{ 3 } $. Step 1: Write $ u^2 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{12u^2}{3} \cdot u^2 & \xlongequal{\text{Step 1}} \frac{12u^2}{3} \cdot \frac{u^2}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 12u^2 \cdot u^2 }{ 3 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 12u^4 }{ 3 } \end{aligned} $$ |
| ③ | Subtract $ \dfrac{12u^4}{3} $ from $ 24u^3 $ to get $ \dfrac{ \color{purple}{ -12u^4+72u^3 } }{ 3 }$. Step 1: Write $ 24u^3 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To subtract raitonal expressions, both fractions must have the same denominator. |
| ④ | Divide $ \dfrac{-12u^4+72u^3}{3} $ by $ 2x+5 $ to get $ \dfrac{ -12u^4+72u^3 }{ 6x+15 } $. 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. $$ \begin{aligned} \frac{ \frac{-12u^4+72u^3}{3} }{2x+5} & \xlongequal{\text{Step 1}} \frac{-12u^4+72u^3}{3} \cdot \frac{\color{blue}{1}}{\color{blue}{2x+5}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( -12u^4+72u^3 \right) \cdot 1 }{ 3 \cdot \left( 2x+5 \right) } \xlongequal{\text{Step 3}} \frac{ -12u^4+72u^3 }{ 6x+15 } \end{aligned} $$ |