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

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+1 }$ and the second by $\color{blue}{ 2x-1 }$.

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