Multiply $5$ by $ \dfrac{x}{4} $ to get $ \dfrac{ 5x }{ 4 } $.

Step 1: Write $ 5 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 5 \cdot \frac{x}{4} & \xlongequal{\text{Step 1}} \frac{5}{\color{red}{1}} \cdot \frac{x}{4} \xlongequal{\text{Step 2}} \frac{ 5 \cdot x }{ 1 \cdot 4 } \xlongequal{\text{Step 3}} \frac{ 5x }{ 4 } \end{aligned} $$

Subtract $ \dfrac{5x}{4} $ from $ \dfrac{6}{x-1} $ to get $ \dfrac{ \color{purple}{ -5x^2+5x+24 } }{ 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}{ 4 }$ and the second by $\color{blue}{ x-1 }$.

$$ \begin{aligned} \frac{6}{x-1} - \frac{5x}{4} & = \frac{ 6 \cdot \color{blue}{ 4 }}{ \left( x-1 \right) \cdot \color{blue}{ 4 }} - \frac{ 5x \cdot \color{blue}{ \left( x-1 \right) }}{ 4 \cdot \color{blue}{ \left( x-1 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 24 } }{ 4x-4 } - \frac{ \color{purple}{ 5x^2-5x } }{ 4x-4 }=\frac{ \color{purple}{ 24 - \left( 5x^2-5x \right) } }{ 4x-4 } = \\[1ex] &=\frac{ \color{purple}{ -5x^2+5x+24 } }{ 4x-4 } \end{aligned} $$