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