a)
[tex]\frac{4-5\sqrt2}{\sqrt2+7} =\frac{4-5\sqrt2}{\sqrt2+7} *\frac{\sqrt2-7}{\sqrt2-7} =\frac{4\sqrt2-28-5*2+35\sqrt2}{2-49}=\frac{39\sqrt2-38}{-47}=\frac{38-39\sqrt2}{47}[/tex]
b)
[tex]\frac{4-5\sqrt2}{\sqrt2+7} =\frac{4-5\sqrt2}{\sqrt2+7} *\frac{4+5\sqrt2}{4+5\sqrt2} =\frac{16-25*2}{4\sqrt2+5*2+28+35\sqrt2}=\frac{-34}{39\sqrt2+38}[/tex]
