Cancel out $\sqrt{7}$ in both numerator and denominator.
$$\frac{\sqrt{7}}{3}+\frac{12}{-7}$$
Fraction $\frac{12}{-7}$ can be rewritten as $-\frac{12}{7}$ by extracting the negative sign.
$$\frac{\sqrt{7}}{3}-\frac{12}{7}$$
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $3$ and $7$ is $21$. Multiply $\frac{\sqrt{7}}{3}$ times $\frac{7}{7}$. Multiply $\frac{12}{7}$ times $\frac{3}{3}$.
$$\frac{7\sqrt{7}}{21}-\frac{12\times 3}{21}$$
Since $\frac{7\sqrt{7}}{21}$ and $\frac{12\times 3}{21}$ have the same denominator, subtract them by subtracting their numerators.
