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