Subtract $ \dfrac{4}{j^2-3} $ from $ j $ to get $ \dfrac{ \color{purple}{ j^3-3j-4 } }{ j^2-3 }$.

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

Step 2: To subtract raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $\color{blue}{ j^2-3 }$.

$$ \begin{aligned} j- \frac{4}{j^2-3} & \xlongequal{\text{Step 1}} \frac{j}{\color{red}{1}} - \frac{4}{j^2-3} = \frac{ j \cdot \color{blue}{ \left( j^2-3 \right) }}{ 1 \cdot \color{blue}{ \left( j^2-3 \right) }} - \frac{ 4 }{ j^2-3 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ j^3-3j } }{ j^2-3 } - \frac{ \color{purple}{ 4 } }{ j^2-3 }=\frac{ \color{purple}{ j^3-3j-4 } }{ j^2-3 } \end{aligned} $$