$$-\dfrac{i}{s}qrt(z^2-1)=\dfrac{iqrtz^2-iqrt}{s}$$
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-\frac{i}{s}qrt(z^2-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{iq}{s}rt(z^2-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{iqr}{s}t(z^2-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{iqrt}{s}(z^2-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}\frac{iqrtz^2-iqrt}{s}\end{aligned} $$ | |
| ① | Multiply $ \dfrac{i}{s} $ by $ q $ to get $ \dfrac{ iq }{ s } $. 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. $$ \begin{aligned} \frac{i}{s} \cdot q & \xlongequal{\text{Step 1}} \frac{i}{s} \cdot \frac{q}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ i \cdot q }{ s \cdot 1 } \xlongequal{\text{Step 3}} \frac{ iq }{ s } \end{aligned} $$ |
| ② | Multiply $ \dfrac{iq}{s} $ by $ r $ to get $ \dfrac{ iqr }{ s } $. 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. $$ \begin{aligned} \frac{iq}{s} \cdot r & \xlongequal{\text{Step 1}} \frac{iq}{s} \cdot \frac{r}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ iq \cdot r }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ iqr }{ s } \end{aligned} $$ |
| ③ | Multiply $ \dfrac{iqr}{s} $ by $ t $ to get $ \dfrac{ iqrt }{ s } $. 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. $$ \begin{aligned} \frac{iqr}{s} \cdot t & \xlongequal{\text{Step 1}} \frac{iqr}{s} \cdot \frac{t}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ iqr \cdot t }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ iqrt }{ s } \end{aligned} $$ |
| ④ | Multiply $ \dfrac{iqrt}{s} $ by $ z^2-1 $ to get $ \dfrac{ iqrtz^2-iqrt }{ s } $. Step 1: Write $ z^2-1 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator. Step 2: Multiply numerators and denominators. Step 3: Simplify numerator and denominator. $$ \begin{aligned} \frac{iqrt}{s} \cdot z^2-1 & \xlongequal{\text{Step 1}} \frac{iqrt}{s} \cdot \frac{z^2-1}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ iqrt \cdot \left( z^2-1 \right) }{ s \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ iqrtz^2-iqrt }{ s } \end{aligned} $$ |