Add $ \dfrac{2}{3x+1} $ and $ \dfrac{x}{x-2} $ to get $ \dfrac{ \color{purple}{ 3x^2+3x-4 } }{ 3x^2-5x-2 }$.

To add raitonal expressions, both fractions must have the same denominator.
We can create a common denominator by multiplying the first fraction by $ \color{blue}{ x-2 }$ and the second by $\color{blue}{ 3x+1 }$.

$$ \begin{aligned} \frac{2}{3x+1} + \frac{x}{x-2} & = \frac{ 2 \cdot \color{blue}{ \left( x-2 \right) }}{ \left( 3x+1 \right) \cdot \color{blue}{ \left( x-2 \right) }} + \frac{ x \cdot \color{blue}{ \left( 3x+1 \right) }}{ \left( x-2 \right) \cdot \color{blue}{ \left( 3x+1 \right) }} = \\[1ex] &=\frac{ \color{purple}{ 2x-4 } }{ 3x^2-6x+x-2 } + \frac{ \color{purple}{ 3x^2+x } }{ 3x^2-6x+x-2 }=\frac{ \color{purple}{ 3x^2+3x-4 } }{ 3x^2-5x-2 } \end{aligned} $$