Consider $\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}+\sqrt{3}\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.
Consider $\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.
Since $\frac{5\left(\sqrt{5}+\sqrt{3}\right)}{2}$ and $\frac{3\left(\sqrt{5}-\sqrt{3}\right)}{2}$ have the same denominator, add them by adding their numerators.
