Question

$\frac{4}{2+ \sqrt{2} } -5+2 \sqrt{2}$

Answer 1

[tex] \frac{4-5(2+ \sqrt{2})+(2 \sqrt{2})(2+ \sqrt{2}) } {2+ \sqrt{2} } = \\ \frac{4-10-5 \sqrt{2}+4 \sqrt{2}+2 \sqrt{2} * \sqrt{2} }{2+ \sqrt{2} } = \\ \frac{-6- \sqrt{2} +4}{2+ \sqrt{2} } = \\ \frac{-2- \sqrt{2} }{2+ \sqrt{2} } = \frac{-(2+ \sqrt{2}) }{2+ \sqrt{2} } = -1 [/tex]