To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\beta $ and $\alpha $ is $\alpha \beta $. Multiply $\frac{\alpha ^{2}}{\beta }$ times $\frac{\alpha }{\alpha }$. Multiply $\frac{\beta ^{2}}{\alpha }$ times $\frac{\beta }{\beta }$.
Since $\frac{\alpha ^{2}\alpha }{\alpha \beta }$ and $\frac{\beta ^{2}\beta }{\alpha \beta }$ have the same denominator, add them by adding their numerators.
