To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $2\left(a+1\right)$ and $4\left(a-1\right)$ is $4\left(a-1\right)\left(a+1\right)$. Multiply $\frac{3}{2\left(a+1\right)}$ times $\frac{2\left(a-1\right)}{2\left(a-1\right)}$. Multiply $\frac{1}{4\left(a-1\right)}$ times $\frac{a+1}{a+1}$.
Since $\frac{3\times 2\left(a-1\right)}{4\left(a-1\right)\left(a+1\right)}$ and $\frac{a+1}{4\left(a-1\right)\left(a+1\right)}$ 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 $4\left(a-1\right)\left(a+1\right)$ and $8\left(a-1\right)\left(-a-1\right)$ is $8\left(a-1\right)\left(a+1\right)$. Multiply $\frac{5a-7}{4\left(a-1\right)\left(a+1\right)}$ times $\frac{2}{2}$. Multiply $\frac{4}{8\left(a-1\right)\left(-a-1\right)}$ times $\frac{-1}{-1}$.
Since $\frac{2\left(5a-7\right)}{8\left(a-1\right)\left(a+1\right)}$ and $\frac{4\left(-1\right)}{8\left(a-1\right)\left(a+1\right)}$ have the same denominator, subtract them by subtracting their numerators.
