$$\frac{30}{\sqrt{2}+\sqrt{3}i}$$

$$=\frac{30}{\sqrt{2}+\sqrt{3}i}·\frac{\sqrt{2}-\sqrt{3}i}{\sqrt{2}-\sqrt{3}}$$

$$=\frac{30·\left(\sqrt{2}-\sqrt{3}i\right)}{{\left(\sqrt{2}\right)}^2-{\left(\sqrt{3}i\right)}^2}$$

$$=\frac{30·\left(\sqrt{2}-\sqrt{3}i\right)}{2-3i^2}$$

$$=\frac{30·\left(\sqrt{2}-\sqrt{3}i\right)}{2-3\left(-1\right)}$$

$$=\frac{30·\left(\sqrt{2}-\sqrt{3}i\right)}{2+3}$$

$$=\frac{30·\left(\sqrt{2}-\sqrt{3}i\right)}{5}$$

$$=6\left(\sqrt{2}-\sqrt{3}i\right)$$