Multiply $2ip$ by $ \dfrac{n}{t} $ to get $ \dfrac{ 2inp }{ t } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 2ip \cdot \frac{n}{t} & \xlongequal{\text{Step 1}} \frac{2ip}{\color{red}{1}} \cdot \frac{n}{t} \xlongequal{\text{Step 2}} \frac{ 2ip \cdot n }{ 1 \cdot t } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 2inp }{ t } \end{aligned} $$

Add $ \dfrac{2inp}{t} $ and $ b $ to get $ \dfrac{ \color{purple}{ 2inp+bt } }{ t }$.

Step 1: Write $ b $ 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 second fraction by $\color{blue}{t}$.

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

Multiply $2np$ by $ \dfrac{2inp+bt}{t} $ to get $ \dfrac{ 4in^2p^2+2bnpt }{ t } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 2np \cdot \frac{2inp+bt}{t} & \xlongequal{\text{Step 1}} \frac{2np}{\color{red}{1}} \cdot \frac{2inp+bt}{t} \xlongequal{\text{Step 2}} \frac{ 2np \cdot \left( 2inp+bt \right) }{ 1 \cdot t } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 4in^2p^2+2bnpt }{ t } \end{aligned} $$

Divide $1$ by $ \dfrac{4in^2p^2+2bnpt}{t} $ to get $ \dfrac{ t }{ 4in^2p^2+2bnpt } $.

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

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

Step 3: Multiply numerators and denominators.

Step 4: Simplify numerator and denominator.

$$ \begin{aligned} \frac{1}{ \frac{\color{blue}{4in^2p^2+2bnpt}}{\color{blue}{t}} } & \xlongequal{\text{Step 1}} 1 \cdot \frac{\color{blue}{t}}{\color{blue}{4in^2p^2+2bnpt}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{1}{\color{red}{1}} \cdot \frac{t}{4in^2p^2+2bnpt} \xlongequal{\text{Step 3}} \frac{ 1 \cdot t }{ 1 \cdot \left( 4in^2p^2+2bnpt \right) } = \\[1ex] & \xlongequal{\text{Step 4}} \frac{ t }{ 4in^2p^2+2bnpt } \end{aligned} $$