Subtract $ \dfrac{9}{8} $ from $ \dfrac{9}{8+x} $ to get $ \dfrac{ \color{purple}{ -9x } }{ 8x+64 }$.

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}{ 8 }$ and the second by $\color{blue}{ x+8 }$.

$$ \begin{aligned} \frac{9}{8+x} - \frac{9}{8} & = \frac{ 9 \cdot \color{blue}{ 8 }}{ \left( 8+x \right) \cdot \color{blue}{ 8 }} - \frac{ 9 \cdot \color{blue}{ \left( x+8 \right) }}{ 8 \cdot \color{blue}{ \left( x+8 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 72 } }{ 64+8x } - \frac{ \color{purple}{ 9x+72 } }{ 64+8x }=\frac{ \color{purple}{ 72 - \left( 9x+72 \right) } }{ 8x+64 } = \\[1ex] &=\frac{ \color{purple}{ -9x } }{ 8x+64 } \end{aligned} $$

Divide $ \dfrac{-9x}{8x+64} $ by $ x $ to get $ \dfrac{ -9x }{ 8x^2+64x } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{-9x}{8x+64} }{x} & \xlongequal{\text{Step 1}} \frac{-9x}{8x+64} \cdot \frac{\color{blue}{1}}{\color{blue}{x}} \xlongequal{\text{Step 2}} \frac{ \left( -9x \right) \cdot 1 }{ \left( 8x+64 \right) \cdot x } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -9x }{ 8x^2+64x } \end{aligned} $$