Multiply $ \dfrac{1}{314i} $ by $ n $ to get $ \dfrac{ n }{ 314i } $.

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

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{1}{314i} \cdot n & \xlongequal{\text{Step 1}} \frac{1}{314i} \cdot \frac{n}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ 1 \cdot n }{ 314i \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ n }{ 314i } \end{aligned} $$

$$ \left( 314i \right)^2 = 314^2i^2 = 98596i^2 $$

Add $p$ and $ \dfrac{n}{314i} $ to get $ \dfrac{ \color{purple}{ 314ip+n } }{ 314i }$.

Step 1: Write $ p $ 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 $\color{blue}{ 314i }$.

$$ \begin{aligned} p+ \frac{n}{314i} & \xlongequal{\text{Step 1}} \frac{p}{\color{red}{1}} + \frac{n}{314i} = \frac{ p \cdot \color{blue}{ 314i }}{ 1 \cdot \color{blue}{ 314i }} + \frac{ n }{ 314i } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 314ip } }{ 314i } + \frac{ \color{purple}{ n } }{ 314i }=\frac{ \color{purple}{ 314ip+n } }{ 314i } \end{aligned} $$

$$ 98596i^2 = 98596 \cdot (-1) = -98596 $$

$$ 98596i^2 = 98596 \cdot (-1) = -98596 $$

Add $ \dfrac{314ip+n}{314i} $ and $ 314di $ to get $ \dfrac{ \color{purple}{ 98596di^2+314ip+n } }{ 314i }$.

Step 1: Write $ 314di $ 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 $\color{blue}{314i}$.

$$ \begin{aligned} \frac{314ip+n}{314i} +314di & \xlongequal{\text{Step 1}} \frac{314ip+n}{314i} + \frac{314di}{\color{red}{1}} = \frac{ 314ip+n }{ 314i } + \frac{ 314di \cdot \color{blue}{ 314i }}{ 1 \cdot \color{blue}{ 314i }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 314ip+n } }{ 314i } + \frac{ \color{purple}{ 98596di^2 } }{ 314i }=\frac{ \color{purple}{ 98596di^2+314ip+n } }{ 314i } \end{aligned} $$

$$ 98596i^2 = 98596 \cdot (-1) = -98596 $$

Combine like terms:

$$ \color{blue}{-98596} 0i+ \color{blue}{1} = \color{blue}{-98595} $$

Divide $ \dfrac{98596di^2+314ip+n}{314i} $ by $ -98595 $ to get $ \dfrac{ 98596di^2+314ip+n }{ -30958830i } $.

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.

$$ \begin{aligned} \frac{ \frac{98596di^2+314ip+n}{314i} }{-98595} & \xlongequal{\text{Step 1}} \frac{98596di^2+314ip+n}{314i} \cdot \frac{\color{blue}{1}}{\color{blue}{-98595}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( 98596di^2+314ip+n \right) \cdot 1 }{ 314i \cdot \left( -98595 \right) } \xlongequal{\text{Step 3}} \frac{ 98596di^2+314ip+n }{ -30958830i } \end{aligned} $$

Multiply $100$ by $ \dfrac{98596di^2+314ip+n}{-30958830i} $ to get $ \dfrac{ 9859600di^2+31400ip+100n }{ -30958830i } $.

Step 1: Write $ 100 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 100 \cdot \frac{98596di^2+314ip+n}{-30958830i} & \xlongequal{\text{Step 1}} \frac{100}{\color{red}{1}} \cdot \frac{98596di^2+314ip+n}{-30958830i} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 100 \cdot \left( 98596di^2+314ip+n \right) }{ 1 \cdot \left( -30958830i \right) } \xlongequal{\text{Step 3}} \frac{ 9859600di^2+31400ip+100n }{ -30958830i } \end{aligned} $$