Subtract $x$ from $ \dfrac{x}{x-10} $ to get $ \dfrac{ \color{purple}{ -x^2+11x } }{ x-10 }$.

Step 1: Write $ x $ 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 second fraction by $\color{blue}{x-10}$.

$$ \begin{aligned} \frac{x}{x-10} -x & \xlongequal{\text{Step 1}} \frac{x}{x-10} - \frac{x}{\color{red}{1}} = \frac{ x }{ x-10 } - \frac{ x \cdot \color{blue}{ \left( x-10 \right) }}{ 1 \cdot \color{blue}{ \left( x-10 \right) }} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ x } }{ x-10 } - \frac{ \color{purple}{ x^2-10x } }{ x-10 }=\frac{ \color{purple}{ x - \left( x^2-10x \right) } }{ x-10 } = \\[1ex] &=\frac{ \color{purple}{ -x^2+11x } }{ x-10 } \end{aligned} $$