Show that 5+18n1+2n\dfrac{5 + \sqrt{18n}}{1 + \sqrt{2n}}1+2n5+18n can be written as 6n−5+22n2n−1\dfrac{6n - 5 + 2\sqrt{2n}}{2n - 1}2n−16n−5+22n where n n\,n is a positive integer.