Since $-\frac{3}{3}$ and $\frac{5}{3}$ have the same denominator, add them by adding their numerators.
$$\frac{\sqrt{6}}{5}+\frac{-3+5}{3}-\frac{7}{3}$$
Add $-3$ and $5$ to get $2$.
$$\frac{\sqrt{6}}{5}+\frac{2}{3}-\frac{7}{3}$$
Since $\frac{2}{3}$ and $\frac{7}{3}$ have the same denominator, subtract them by subtracting their numerators.
$$\frac{\sqrt{6}}{5}+\frac{2-7}{3}$$
Subtract $7$ from $2$ to get $-5$.
$$\frac{\sqrt{6}}{5}-\frac{5}{3}$$
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $5$ and $3$ is $15$. Multiply $\frac{\sqrt{6}}{5}$ times $\frac{3}{3}$. Multiply $\frac{5}{3}$ times $\frac{5}{5}$.
$$\frac{3\sqrt{6}}{15}-\frac{5\times 5}{15}$$
Since $\frac{3\sqrt{6}}{15}$ and $\frac{5\times 5}{15}$ have the same denominator, subtract them by subtracting their numerators.
