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

Step 1: Write $ b-3 $ 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 $\color{blue}{ b^2 }$.

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