Multiply $ \color{blue}{5} $ by $ \left( x+4\right) $ $$ \color{blue}{5} \cdot \left( x+4\right) = 5x+20 $$

Remove the parentheses by changing the sign of each term within them.

$$ - \left( 5x+20 \right) = -5x-20 $$

Combine like terms:

$$ \color{blue}{7x} \color{blue}{-5x} -20 = \color{blue}{2x} -20 $$

Subtract $ \dfrac{x+5}{2x-20} $ from $ 6 $ to get $ \dfrac{ \color{purple}{ 11x-125 } }{ 2x-20 }$.

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 $\color{blue}{ 2x-20 }$.

$$ \begin{aligned} 6- \frac{x+5}{2x-20} & \xlongequal{\text{Step 1}} \frac{6}{\color{red}{1}} - \frac{x+5}{2x-20} = \frac{ 6 \cdot \color{blue}{ \left( 2x-20 \right) }}{ 1 \cdot \color{blue}{ \left( 2x-20 \right) }} - \frac{ x+5 }{ 2x-20 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 12x-120 } }{ 2x-20 } - \frac{ \color{purple}{ x+5 } }{ 2x-20 }=\frac{ \color{purple}{ 12x-120 - \left( x+5 \right) } }{ 2x-20 } = \\[1ex] &=\frac{ \color{purple}{ 11x-125 } }{ 2x-20 } \end{aligned} $$