Multiply $10$ by $ \dfrac{x}{4x+9} $ to get $ \dfrac{ 10x }{ 4x+9 } $.

Step 1: Write $ 10 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 10 \cdot \frac{x}{4x+9} & \xlongequal{\text{Step 1}} \frac{10}{\color{red}{1}} \cdot \frac{x}{4x+9} \xlongequal{\text{Step 2}} \frac{ 10 \cdot x }{ 1 \cdot \left( 4x+9 \right) } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 10x }{ 4x+9 } \end{aligned} $$

Subtract $ \dfrac{10x}{4x+9} $ from $ 8 $ to get $ \dfrac{ \color{purple}{ 22x+72 } }{ 4x+9 }$.

Step 1: Write $ 8 $ 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 $\color{blue}{ 4x+9 }$.

$$ \begin{aligned} 8- \frac{10x}{4x+9} & \xlongequal{\text{Step 1}} \frac{8}{\color{red}{1}} - \frac{10x}{4x+9} = \frac{ 8 \cdot \color{blue}{ \left( 4x+9 \right) }}{ 1 \cdot \color{blue}{ \left( 4x+9 \right) }} - \frac{ 10x }{ 4x+9 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 32x+72 } }{ 4x+9 } - \frac{ \color{purple}{ 10x } }{ 4x+9 }=\frac{ \color{purple}{ 22x+72 } }{ 4x+9 } \end{aligned} $$