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 $7$ and $3$ is $21$. Multiply $\frac{5\left(3-\sqrt{2}\right)}{7}$ times $\frac{3}{3}$. Multiply $\frac{\sqrt{2}}{3}$ times $\frac{7}{7}$.
Since $\frac{3\times 5\left(3-\sqrt{2}\right)}{21}$ and $\frac{7\sqrt{2}}{21}$ have the same denominator, subtract them by subtracting their numerators.
