$$ i^2 = -1 $$

Divide $ \dfrac{-1}{1} $ by $ 4 $ to get $ \dfrac{-1}{4} $.

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

Step 2: Multiply numerators and denominators.

$$ \begin{aligned} \frac{ \frac{-1}{1} }{4} = \frac{-1}{1} \cdot \frac{\color{blue}{1}}{\color{blue}{4}} = \frac{-1}{4} \end{aligned} $$

Subtract $ \dfrac{4}{i} $ from $ \dfrac{-1}{4} $ to get $ \dfrac{ \color{purple}{ -i-16 } }{ 4i }$.

To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ i }$ and the second by $\color{blue}{ 4 }$.

$$ \begin{aligned} \frac{-1}{4} - \frac{4}{i} & = \frac{ \left( -1 \right) \cdot \color{blue}{ i }}{ 4 \cdot \color{blue}{ i }} - \frac{ 4 \cdot \color{blue}{ 4 }}{ i \cdot \color{blue}{ 4 }} = \\[1ex] &=\frac{ \color{purple}{ -i } }{ 4i } - \frac{ \color{purple}{ 16 } }{ 4i }=\frac{ \color{purple}{ -i-16 } }{ 4i } \end{aligned} $$

Divide $ \, -16-i \, $ by $ \, 4i \, $ to get $\,\, \dfrac{-1+16i}{4} $.
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