To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(x+1\right)\left(2x+3\right)$ and $3\left(x+1\right)$ is $3\left(x+1\right)\left(2x+3\right)$. Multiply $\frac{2x-1}{\left(x+1\right)\left(2x+3\right)}$ times $\frac{3}{3}$. Multiply $\frac{2}{3\left(x+1\right)}$ times $\frac{2x+3}{2x+3}$.
Since $\frac{3\left(2x-1\right)}{3\left(x+1\right)\left(2x+3\right)}$ and $\frac{2\left(2x+3\right)}{3\left(x+1\right)\left(2x+3\right)}$ have the same denominator, add them by adding their numerators.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(x+1\right)\left(2x+3\right)$ and $3\left(x+1\right)$ is $3\left(x+1\right)\left(2x+3\right)$. Multiply $\frac{2x-1}{\left(x+1\right)\left(2x+3\right)}$ times $\frac{3}{3}$. Multiply $\frac{2}{3\left(x+1\right)}$ times $\frac{2x+3}{2x+3}$.
Since $\frac{3\left(2x-1\right)}{3\left(x+1\right)\left(2x+3\right)}$ and $\frac{2\left(2x+3\right)}{3\left(x+1\right)\left(2x+3\right)}$ have the same denominator, add them by adding their numerators.
