Subtract $ \dfrac{5}{x-10} $ from $ 3x+2 $ to get $ \dfrac{ \color{purple}{ 3x^2-28x-25 } }{ x-10 }$.

Step 1: Write $ 3x+2 $ 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 $\color{blue}{ x-10 }$.

$$ \begin{aligned} 3x+2- \frac{5}{x-10} & \xlongequal{\text{Step 1}} \frac{3x+2}{\color{red}{1}} - \frac{5}{x-10} = \frac{ \left( 3x+2 \right) \cdot \color{blue}{ \left( x-10 \right) }}{ 1 \cdot \color{blue}{ \left( x-10 \right) }} - \frac{ 5 }{ x-10 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3x^2-30x+2x-20 } }{ x-10 } - \frac{ \color{purple}{ 5 } }{ x-10 }=\frac{ \color{purple}{ 3x^2-28x-25 } }{ x-10 } \end{aligned} $$