\(Express $2 + \sqrt{2} + \frac{1}{2 + \sqrt{2}} + \frac{1}{\sqrt{2} - 2}$ in simplest form.\)
Look at the last two fractions
The sum of these = [ √2 - 2] + [ √2 + 2 ] 2√2 2√2
________________ = _____ = ___ = - √2
[ √2+ 2 ] [√2 - 2 ] 2 - 4 -2
So.....we just have
2 + √2 - √2 =
2