To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(x-3\right)\left(x+2\right)$ and $\left(x+2\right)\left(4-x\right)$ is $\left(x-3\right)\left(x+2\right)\left(-x+4\right)$. Multiply $\frac{1}{\left(x-3\right)\left(x+2\right)}$ times $\frac{-x+4}{-x+4}$. Multiply $\frac{3}{\left(x+2\right)\left(4-x\right)}$ times $\frac{x-3}{x-3}$.
Since $\frac{-x+4}{\left(x-3\right)\left(x+2\right)\left(-x+4\right)}$ and $\frac{3\left(x-3\right)}{\left(x-3\right)\left(x+2\right)\left(-x+4\right)}$ 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 $\left(x-3\right)\left(x+2\right)$ and $\left(x+2\right)\left(4-x\right)$ is $\left(x-3\right)\left(x+2\right)\left(-x+4\right)$. Multiply $\frac{1}{\left(x-3\right)\left(x+2\right)}$ times $\frac{-x+4}{-x+4}$. Multiply $\frac{3}{\left(x+2\right)\left(4-x\right)}$ times $\frac{x-3}{x-3}$.
Since $\frac{-x+4}{\left(x-3\right)\left(x+2\right)\left(-x+4\right)}$ and $\frac{3\left(x-3\right)}{\left(x-3\right)\left(x+2\right)\left(-x+4\right)}$ have the same denominator, add them by adding their numerators.
