[tex]\sqrt b- \sqrt a +\frac{1}{\sqrt a+\sqrt b}=\sqrt b- \sqrt a +\frac{1}{\sqrt a+\sqrt b}\cdot\frac{\sqrt a-\sqrt b}{\sqrt a-\sqrt b}=\sqrt b- \sqrt a +\frac{\sqrt a-\sqrt b}{a-b}=\\\\\\\sqrt b- \sqrt a +\frac{\sqrt a-\sqrt b}{1}=\sqrt b- \sqrt a +\sqrt a-\sqrt b=0\in C[/tex]
