Add $ \dfrac{5}{2x+1} $ and $ \dfrac{3}{2-4x} $ to get $ \dfrac{ \color{purple}{ -14x+13 } }{ -8x^2+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}{ -4x+2 }$ and the second by $\color{blue}{ 2x+1 }$.

$$ \begin{aligned} \frac{5}{2x+1} + \frac{3}{2-4x} & = \frac{ 5 \cdot \color{blue}{ \left( -4x+2 \right) }}{ \left( 2x+1 \right) \cdot \color{blue}{ \left( -4x+2 \right) }} + \frac{ 3 \cdot \color{blue}{ \left( 2x+1 \right) }}{ \left( 2-4x \right) \cdot \color{blue}{ \left( 2x+1 \right) }} = \\[1ex] &=\frac{ \color{purple}{ -20x+10 } }{ -8x^2+ \cancel{4x} -\cancel{4x}+2 } + \frac{ \color{purple}{ 6x+3 } }{ -8x^2+ \cancel{4x} -\cancel{4x}+2 } = \\[1ex] &=\frac{ \color{purple}{ -14x+13 } }{ -8x^2+2 } \end{aligned} $$