Algebra
# Radical Expressions and Equations

Given that $a>0$, $b>0$, and $\sqrt{ab}=4$, evaluate

$\frac1b \sqrt{\frac{b}{a}} - \frac3a \sqrt{\frac{a}{b}}.$

Simplify $\frac{\sqrt{7}}{\sqrt{7}+\sqrt{6}}+7+\sqrt{42}.$

Simplify

$\frac{1}{\sqrt[3]{2}-1} - \frac{\sqrt[3]{2}}{\sqrt[3]{4} + \sqrt[3]{2} + 1}.$

Evaluate the above expression.

Simplify $\frac{12+\sqrt{17}}{12-\sqrt{17}} = \frac{a}{c} + \frac{b}{c}\sqrt{17}$.