Subtract $ \dfrac{7}{x-4} $ from $ 3x+2 $ to get $ \dfrac{ \color{purple}{ 3x^2-10x-15 } }{ x-4 }$.

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 $\color{blue}{ x-4 }$.

$$ \begin{aligned} 3x+2- \frac{7}{x-4} & \xlongequal{\text{Step 1}} \frac{3x+2}{\color{red}{1}} - \frac{7}{x-4} = \frac{ \left( 3x+2 \right) \cdot \color{blue}{ \left( x-4 \right) }}{ 1 \cdot \color{blue}{ \left( x-4 \right) }} - \frac{ 7 }{ x-4 } = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \color{purple}{ 3x^2-12x+2x-8 } }{ x-4 } - \frac{ \color{purple}{ 7 } }{ x-4 }=\frac{ \color{purple}{ 3x^2-10x-15 } }{ x-4 } \end{aligned} $$