# Rationalizing Denominators in Rational Expressions

Fully rationalize and simplify the following fractions:

1. $\dfrac{4}{\sqrt{6}}$

2. $\dfrac{x}{\sqrt{3}}$

3. $\dfrac{2}{\sqrt{12}}$

4. $\dfrac{3}{i}$

5. $\dfrac{2}{6i}$

6. $\dfrac{5}{\sqrt{6}+2}$

7. $\dfrac{1}{\sqrt{3}-5}$

8. $\dfrac{1}{4+2\sqrt{4}}$

9. $\dfrac{1}{5-3\sqrt{2}}$

10. $\dfrac{3}{i+\sqrt{7}}$