Subtract $ \dfrac{1}{x-6} $ from $ 5x $ to get $ \dfrac{ \color{purple}{ 5x^2-30x-1 } }{ x-6 }$.

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

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