Radicals in Fractions - Rationalizing Denominators w/ Complex Conjugates
Rationalize the denominators in the following fractions:
- $\dfrac{3+\sqrt{17}}{2-3\sqrt{17}}$
- $\dfrac{11+\sqrt{7}}{\sqrt{2}+\sqrt{5}}$
- $\dfrac{4+\sqrt{10}}{\sqrt{2}+\sqrt{5}}$
- $\dfrac{6}{3+4i}$
- $\dfrac{7+5i}{2-2i}$
- $\dfrac{9-9i}{9+9i}$
- $\dfrac{3+\sqrt[3]{4}}{\sqrt[3]{5}}$
- $\dfrac{6-\sqrt{35}}{\sqrt{5}-\sqrt{7}}$
- $\dfrac{5-2i}{3+3i}$
- $\dfrac{2+2i}{3i}$