$$\dfrac{\dfrac{3-\dfrac{4}{t^2}}{1}}{s}qrtt=\dfrac{3qrt^4-4qrt^2}{st^2}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{\frac{3-\frac{4}{t^2}}{1}}{s}qrtt& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{\frac{\frac{3t^2-4}{t^2}}{1}}{s}qrtt \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{\frac{3t^2-4}{t^2}}{s}qrtt \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{3t^2-4}{st^2}qrtt \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{3qt^2-4q}{st^2}rtt \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}\frac{3qrt^2-4qr}{st^2}tt \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}\frac{3qrt^3-4qrt}{st^2}t \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}\frac{3qrt^4-4qrt^2}{st^2}\end{aligned} $$ | |
| ① | Subtract $ \dfrac{4}{t^2} $ from $ 3 $ to get $ \dfrac{ \color{purple}{ 3t^2-4 } }{ t^2 }$. Step 1: Write $ 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. |
| ② | Divide $ \dfrac{3t^2-4}{t^2} $ by $ 1 $ to get $ \dfrac{ 3t^2-4 }{ t^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. $$ \begin{aligned} \frac{ \frac{3t^2-4}{t^2} }{1} & \xlongequal{\text{Step 1}} \frac{3t^2-4}{t^2} \cdot \frac{\color{blue}{1}}{\color{blue}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 3t^2-4 \right) \cdot 1 }{ t^2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3t^2-4 }{ t^2 } \end{aligned} $$ |
| ③ | Divide $ \dfrac{3t^2-4}{t^2} $ by $ s $ to get $ \dfrac{ 3t^2-4 }{ st^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. $$ \begin{aligned} \frac{ \frac{3t^2-4}{t^2} }{s} & \xlongequal{\text{Step 1}} \frac{3t^2-4}{t^2} \cdot \frac{\color{blue}{1}}{\color{blue}{s}} \xlongequal{\text{Step 2}} \frac{ \left( 3t^2-4 \right) \cdot 1 }{ t^2 \cdot s } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3t^2-4 }{ st^2 } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{3t^2-4}{st^2} $ by $ q $ to get $ \dfrac{ 3qt^2-4q }{ st^2 } $. Step 1: Write $ q $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{3t^2-4}{st^2} \cdot q & \xlongequal{\text{Step 1}} \frac{3t^2-4}{st^2} \cdot \frac{q}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 3t^2-4 \right) \cdot q }{ st^2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3qt^2-4q }{ st^2 } \end{aligned} $$ |
| ⑤ | Multiply $ \dfrac{3qt^2-4q}{st^2} $ by $ r $ to get $ \dfrac{ 3qrt^2-4qr }{ st^2 } $. Step 1: Write $ r $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{3qt^2-4q}{st^2} \cdot r & \xlongequal{\text{Step 1}} \frac{3qt^2-4q}{st^2} \cdot \frac{r}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 3qt^2-4q \right) \cdot r }{ st^2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3qrt^2-4qr }{ st^2 } \end{aligned} $$ |
| ⑥ | Multiply $ \dfrac{3qrt^2-4qr}{st^2} $ by $ t $ to get $ \dfrac{ 3qrt^3-4qrt }{ st^2 } $. Step 1: Write $ t $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{3qrt^2-4qr}{st^2} \cdot t & \xlongequal{\text{Step 1}} \frac{3qrt^2-4qr}{st^2} \cdot \frac{t}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 3qrt^2-4qr \right) \cdot t }{ st^2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3qrt^3-4qrt }{ st^2 } \end{aligned} $$ |
| ⑦ | Multiply $ \dfrac{3qrt^3-4qrt}{st^2} $ by $ t $ to get $ \dfrac{ 3qrt^4-4qrt^2 }{ st^2 } $. Step 1: Write $ t $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{3qrt^3-4qrt}{st^2} \cdot t & \xlongequal{\text{Step 1}} \frac{3qrt^3-4qrt}{st^2} \cdot \frac{t}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 3qrt^3-4qrt \right) \cdot t }{ st^2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 3qrt^4-4qrt^2 }{ st^2 } \end{aligned} $$ |