$$iw\dfrac{niw+2e}{iw+\dfrac{1}{t}}=\dfrac{i^2ntw^2+2eitw}{itw+1}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}iw\frac{niw+2e}{iw+\frac{1}{t}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}iw\frac{niw+2e}{\frac{itw+1}{t}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}iw\frac{intw+2et}{itw+1} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{i^2ntw^2+2eitw}{itw+1}\end{aligned} $$ | |
| ① | Add $iw$ and $ \dfrac{1}{t} $ to get $ \dfrac{ \color{purple}{ itw+1 } }{ t }$. Step 1: Write $ iw $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: To add raitonal expressions, both fractions must have the same denominator. |
| ② | Divide $inw+2e$ by $ \dfrac{itw+1}{t} $ to get $ \dfrac{ intw+2et }{ itw+1 } $. Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction. Step 2: Write $ inw+2e $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 3: Multiply numerators and denominators. Step 4: Simplify numerator and denominator. $$ \begin{aligned} \frac{inw+2e}{ \frac{\color{blue}{itw+1}}{\color{blue}{t}} } & \xlongequal{\text{Step 1}} inw+2e \cdot \frac{\color{blue}{t}}{\color{blue}{itw+1}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{inw+2e}{\color{red}{1}} \cdot \frac{t}{itw+1} \xlongequal{\text{Step 3}} \frac{ \left( inw+2e \right) \cdot t }{ 1 \cdot \left( itw+1 \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ intw+2et }{ itw+1 } \end{aligned} $$ |
| ③ | Multiply $iw$ by $ \dfrac{intw+2et}{itw+1} $ to get $ \dfrac{ i^2ntw^2+2eitw }{ itw+1 } $. Step 1: Write $ iw $ as a fraction by putting $ \color{red}{1} $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} iw \cdot \frac{intw+2et}{itw+1} & \xlongequal{\text{Step 1}} \frac{iw}{\color{red}{1}} \cdot \frac{intw+2et}{itw+1} \xlongequal{\text{Step 2}} \frac{ iw \cdot \left( intw+2et \right) }{ 1 \cdot \left( itw+1 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ i^2ntw^2+2eitw }{ itw+1 } \end{aligned} $$ |