Multiply $2p$ by $ \dfrac{i}{5} $ to get $ \dfrac{ 2ip }{ 5 } $.

Step 1: Write $ 2p $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 2p \cdot \frac{i}{5} & \xlongequal{\text{Step 1}} \frac{2p}{\color{red}{1}} \cdot \frac{i}{5} \xlongequal{\text{Step 2}} \frac{ 2p \cdot i }{ 1 \cdot 5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2ip }{ 5 } \end{aligned} $$

Multiply $2p$ by $ \dfrac{i}{5} $ to get $ \dfrac{ 2ip }{ 5 } $.

Step 1: Write $ 2p $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 2p \cdot \frac{i}{5} & \xlongequal{\text{Step 1}} \frac{2p}{\color{red}{1}} \cdot \frac{i}{5} \xlongequal{\text{Step 2}} \frac{ 2p \cdot i }{ 1 \cdot 5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2ip }{ 5 } \end{aligned} $$

Multiply $cos$ by $ \dfrac{2ip}{5} $ to get $ \dfrac{ 2ciops }{ 5 } $.

Step 1: Write $ cos $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} cos \cdot \frac{2ip}{5} & \xlongequal{\text{Step 1}} \frac{cos}{\color{red}{1}} \cdot \frac{2ip}{5} \xlongequal{\text{Step 2}} \frac{ cos \cdot 2ip }{ 1 \cdot 5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2ciops }{ 5 } \end{aligned} $$

Multiply $ins$ by $ \dfrac{2ip}{5} $ to get $ \dfrac{ 2i^2nps }{ 5 } $.

Step 1: Write $ ins $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} ins \cdot \frac{2ip}{5} & \xlongequal{\text{Step 1}} \frac{ins}{\color{red}{1}} \cdot \frac{2ip}{5} \xlongequal{\text{Step 2}} \frac{ ins \cdot 2ip }{ 1 \cdot 5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2i^2nps }{ 5 } \end{aligned} $$

Add $1$ and $ \dfrac{2ciops}{5} $ to get $ \dfrac{ \color{purple}{ 2ciops+5 } }{ 5 }$.

Step 1: Write $ 1 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ 5 }$.

$$ \begin{aligned} 1+ \frac{2ciops}{5} & \xlongequal{\text{Step 1}} \frac{1}{\color{red}{1}} + \frac{2ciops}{5} = \frac{ 1 \cdot \color{blue}{ 5 }}{ 1 \cdot \color{blue}{ 5 }} + \frac{ 2ciops }{ 5 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 5 } }{ 5 } + \frac{ \color{purple}{ 2ciops } }{ 5 }=\frac{ \color{purple}{ 2ciops+5 } }{ 5 } \end{aligned} $$

Multiply $ins$ by $ \dfrac{2ip}{5} $ to get $ \dfrac{ 2i^2nps }{ 5 } $.

Step 1: Write $ ins $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} ins \cdot \frac{2ip}{5} & \xlongequal{\text{Step 1}} \frac{ins}{\color{red}{1}} \cdot \frac{2ip}{5} \xlongequal{\text{Step 2}} \frac{ ins \cdot 2ip }{ 1 \cdot 5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2i^2nps }{ 5 } \end{aligned} $$

Multiply $ \dfrac{2ciops+5}{5} $ by $ i $ to get $ \dfrac{ 2ci^2ops+5i }{ 5 } $.

Step 1: Write $ i $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{2ciops+5}{5} \cdot i & \xlongequal{\text{Step 1}} \frac{2ciops+5}{5} \cdot \frac{i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 2ciops+5 \right) \cdot i }{ 5 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2ci^2ops+5i }{ 5 } \end{aligned} $$

Multiply $ins$ by $ \dfrac{2ip}{5} $ to get $ \dfrac{ 2i^2nps }{ 5 } $.

Step 1: Write $ ins $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} ins \cdot \frac{2ip}{5} & \xlongequal{\text{Step 1}} \frac{ins}{\color{red}{1}} \cdot \frac{2ip}{5} \xlongequal{\text{Step 2}} \frac{ ins \cdot 2ip }{ 1 \cdot 5 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2i^2nps }{ 5 } \end{aligned} $$

Add $ \dfrac{2ci^2ops+5i}{5} $ and $ \dfrac{2i^2nps}{5} $ to get $ \dfrac{2ci^2ops+2i^2nps+5i}{5} $.

To add expressions with the same denominators, we add the numerators and write the result over the common denominator.

$$ \begin{aligned} \frac{2ci^2ops+5i}{5} + \frac{2i^2nps}{5} & = \frac{2ci^2ops+5i}{\color{blue}{5}} + \frac{2i^2nps}{\color{blue}{5}} = \\[1ex] &=\frac{ 2ci^2ops+5i + 2i^2nps }{ \color{blue}{ 5 }}= \frac{2ci^2ops+2i^2nps+5i}{5} \end{aligned} $$

Divide $i-1$ by $ \dfrac{2ci^2ops+2i^2nps+5i}{5} $ to get $ \dfrac{ 5i-5 }{ 2ci^2ops+2i^2nps+5i } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Write $ i-1 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{i-1}{ \frac{\color{blue}{2ci^2ops+2i^2nps+5i}}{\color{blue}{5}} } & \xlongequal{\text{Step 1}} i-1 \cdot \frac{\color{blue}{5}}{\color{blue}{2ci^2ops+2i^2nps+5i}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{i-1}{\color{red}{1}} \cdot \frac{5}{2ci^2ops+2i^2nps+5i} \xlongequal{\text{Step 3}} \frac{ \left( i-1 \right) \cdot 5 }{ 1 \cdot \left( 2ci^2ops+2i^2nps+5i \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ 5i-5 }{ 2ci^2ops+2i^2nps+5i } \end{aligned} $$