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