Subtract $ \dfrac{7}{x+1} $ from $ \dfrac{1}{4} $ to get $ \dfrac{ \color{purple}{ x-27 } }{ 4x+4 }$.

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}{ x+1 }$ and the second by $\color{blue}{ 4 }$.

$$ \begin{aligned} \frac{1}{4} - \frac{7}{x+1} & = \frac{ 1 \cdot \color{blue}{ \left( x+1 \right) }}{ 4 \cdot \color{blue}{ \left( x+1 \right) }} - \frac{ 7 \cdot \color{blue}{ 4 }}{ \left( x+1 \right) \cdot \color{blue}{ 4 }} = \\[1ex] &=\frac{ \color{purple}{ x+1 } }{ 4x+4 } - \frac{ \color{purple}{ 28 } }{ 4x+4 }=\frac{ \color{purple}{ x-27 } }{ 4x+4 } \end{aligned} $$

Divide $ \dfrac{20}{x+1} $ by $ \dfrac{x-27}{4x+4} $ to get $ \dfrac{ 80 }{ x-27 } $.

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

Step 2: Factor numerators and denominators.

Step 3: Cancel common factors.

Step 4: Multiply numerators and denominators.

Step 5: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{20}{x+1} }{ \frac{\color{blue}{x-27}}{\color{blue}{4x+4}} } & \xlongequal{\text{Step 1}} \frac{20}{x+1} \cdot \frac{\color{blue}{4x+4}}{\color{blue}{x-27}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 20 }{ 1 \cdot \color{red}{ \left( x+1 \right) } } \cdot \frac{ 4 \cdot \color{red}{ \left( x+1 \right) } }{ x-27 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 20 }{ 1 } \cdot \frac{ 4 }{ x-27 } \xlongequal{\text{Step 4}} \frac{ 20 \cdot 4 }{ 1 \cdot \left( x-27 \right) } \xlongequal{\text{Step 5}} \frac{ 80 }{ x-27 } \end{aligned} $$