Consider $\left(9+\sqrt{3}\right)\left(9-\sqrt{3}\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.
Consider $\left(3+\sqrt{2}\right)\left(3-\sqrt{2}\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $78$ and $7$ is $546$. Multiply $\frac{9-\sqrt{3}}{78}$ times $\frac{7}{7}$. Multiply $\frac{3-\sqrt{2}}{7}$ times $\frac{78}{78}$.
Since $\frac{7\left(9-\sqrt{3}\right)}{546}$ and $\frac{78\left(3-\sqrt{2}\right)}{546}$ have the same denominator, add them by adding their numerators.
