Subtract $ \dfrac{6}{d} $ from $ d $ to get $ \dfrac{ \color{purple}{ d^2-6 } }{ d }$.

Step 1: Write $ d $ 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 $\color{blue}{ d }$.

$$ \begin{aligned} d- \frac{6}{d} & \xlongequal{\text{Step 1}} \frac{d}{\color{red}{1}} - \frac{6}{d} = \frac{ d \cdot \color{blue}{ d }}{ 1 \cdot \color{blue}{ d }} - \frac{ 6 }{ d } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ d^2 } }{ d } - \frac{ \color{purple}{ 6 } }{ d }=\frac{ \color{purple}{ d^2-6 } }{ d } \end{aligned} $$

Subtract $5$ from $ \dfrac{d^2-6}{d} $ to get $ \dfrac{ \color{purple}{ d^2-5d-6 } }{ d }$.

Step 1: Write $ 5 $ 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 second fraction by $\color{blue}{d}$.

$$ \begin{aligned} \frac{d^2-6}{d} -5 & \xlongequal{\text{Step 1}} \frac{d^2-6}{d} - \frac{5}{\color{red}{1}} = \frac{ d^2-6 }{ d } - \frac{ 5 \cdot \color{blue}{ d }}{ 1 \cdot \color{blue}{ d }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ d^2-6 } }{ d } - \frac{ \color{purple}{ 5d } }{ d }=\frac{ \color{purple}{ d^2-5d-6 } }{ d } \end{aligned} $$