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 $\frac{4}{a+1}$ times $\frac{a-1}{a-1}$.
Since $\frac{3\left(a+1\right)}{\left(a-1\right)\left(a+1\right)}$ and $\frac{4\left(a-1\right)}{\left(a-1\right)\left(a+1\right)}$ have the same denominator, add them by adding their numerators.
Since $\frac{7a-1}{\left(a-1\right)\left(a+1\right)}$ and $\frac{a+2}{\left(a-1\right)\left(a+1\right)}$ 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 $a-1$ and $a+1$ is $\left(a-1\right)\left(a+1\right)$. Multiply $\frac{3}{a-1}$ times $\frac{a+1}{a+1}$. Multiply $\frac{4}{a+1}$ times $\frac{a-1}{a-1}$.
Since $\frac{3\left(a+1\right)}{\left(a-1\right)\left(a+1\right)}$ and $\frac{4\left(a-1\right)}{\left(a-1\right)\left(a+1\right)}$ have the same denominator, add them by adding their numerators.
Since $\frac{7a-1}{\left(a-1\right)\left(a+1\right)}$ and $\frac{a+2}{\left(a-1\right)\left(a+1\right)}$ have the same denominator, add them by adding their numerators.
