Subtract $a$ from $ \dfrac{4}{9a-8} $ to get $ \dfrac{ \color{purple}{ -9a^2+8a+4 } }{ 9a-8 }$.

Step 1: Write $ a $ 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 $\color{blue}{9a-8}$.

$$ \begin{aligned} \frac{4}{9a-8} -a & \xlongequal{\text{Step 1}} \frac{4}{9a-8} - \frac{a}{\color{red}{1}} = \frac{ 4 }{ 9a-8 } - \frac{ a \cdot \color{blue}{ \left( 9a-8 \right) }}{ 1 \cdot \color{blue}{ \left( 9a-8 \right) }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 4 } }{ 9a-8 } - \frac{ \color{purple}{ 9a^2-8a } }{ 9a-8 }=\frac{ \color{purple}{ 4 - \left( 9a^2-8a \right) } }{ 9a-8 } = \\[1ex] &=\frac{ \color{purple}{ -9a^2+8a+4 } }{ 9a-8 } \end{aligned} $$