To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x\left(x+1\right)$ and $\left(x+2\right)\left(x+3\right)$ is $x\left(x+1\right)\left(x+2\right)\left(x+3\right)$. Multiply $\frac{1}{x\left(x+1\right)}$ times $\frac{\left(x+2\right)\left(x+3\right)}{\left(x+2\right)\left(x+3\right)}$. Multiply $\frac{2x+5}{\left(x+2\right)\left(x+3\right)}$ times $\frac{x\left(x+1\right)}{x\left(x+1\right)}$.
Since $\frac{\left(x+2\right)\left(x+3\right)}{x\left(x+1\right)\left(x+2\right)\left(x+3\right)}$ and $\frac{\left(2x+5\right)x\left(x+1\right)}{x\left(x+1\right)\left(x+2\right)\left(x+3\right)}$ have the same denominator, subtract them by subtracting their numerators.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x\left(x+1\right)$ and $\left(x+2\right)\left(x+3\right)$ is $x\left(x+1\right)\left(x+2\right)\left(x+3\right)$. Multiply $\frac{1}{x\left(x+1\right)}$ times $\frac{\left(x+2\right)\left(x+3\right)}{\left(x+2\right)\left(x+3\right)}$. Multiply $\frac{2x+5}{\left(x+2\right)\left(x+3\right)}$ times $\frac{x\left(x+1\right)}{x\left(x+1\right)}$.
Since $\frac{\left(x+2\right)\left(x+3\right)}{x\left(x+1\right)\left(x+2\right)\left(x+3\right)}$ and $\frac{\left(2x+5\right)x\left(x+1\right)}{x\left(x+1\right)\left(x+2\right)\left(x+3\right)}$ have the same denominator, subtract them by subtracting their numerators.
