Rationalize denominator simple

In this question you should show all stages of your working. Solutions relying on calculator technology are not acceptable. Simplify $$\frac{\sqrt{32} + \sqrt{18}}{3 + \sqrt{2}}$$ giving your answer in the form \(b\sqrt{2} + c\), where \(b\) and \(c\) are integers. [5]

In this question you must show detailed reasoning. Express \(\frac{8 + \sqrt{7}}{2 + \sqrt{7}}\) in the form \(a + b\sqrt{7}\), where \(a\) and \(b\) are integers. [4]

This question requires detailed reasoning. Express \(\frac{3 + \sqrt{20}}{3 + \sqrt{5}}\) in the form \(a + b\sqrt{5}\). [4]

In this question you must show detailed reasoning. Simplify \(10 + 7\sqrt{5} + \frac{38}{1 - 2\sqrt{5}}\), giving your answer in the form \(a + b\sqrt{5}\). [3]