Multiply $ \dfrac{x+5}{7x-5} $ by $ x+4 $ to get $ \dfrac{x^2+9x+20}{7x-5} $.

Step 1: Write $ x+4 $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{x+5}{7x-5} \cdot x+4 & \xlongequal{\text{Step 1}} \frac{x+5}{7x-5} \cdot \frac{x+4}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( x+5 \right) \cdot \left( x+4 \right) }{ \left( 7x-5 \right) \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ x^2+4x+5x+20 }{ 7x-5 } = \frac{x^2+9x+20}{7x-5} \end{aligned} $$

Subtract $ \dfrac{x^2+9x+20}{7x-5} $ from $ 6 $ to get $ \dfrac{ \color{purple}{ -x^2+33x-50 } }{ 7x-5 }$.

Step 1: Write $ 6 $ 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 $\color{blue}{ 7x-5 }$.

$$ \begin{aligned} 6- \frac{x^2+9x+20}{7x-5} & \xlongequal{\text{Step 1}} \frac{6}{\color{red}{1}} - \frac{x^2+9x+20}{7x-5} = \frac{ 6 \cdot \color{blue}{ \left( 7x-5 \right) }}{ 1 \cdot \color{blue}{ \left( 7x-5 \right) }} - \frac{ x^2+9x+20 }{ 7x-5 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 42x-30 } }{ 7x-5 } - \frac{ \color{purple}{ x^2+9x+20 } }{ 7x-5 }=\frac{ \color{purple}{ 42x-30 - \left( x^2+9x+20 \right) } }{ 7x-5 } = \\[1ex] &=\frac{ \color{purple}{ -x^2+33x-50 } }{ 7x-5 } \end{aligned} $$