Question

(\(\frac{1}{\sqrt{x}+2}+\frac{1}{\sqrt{x}-2}\)) . \(\frac{\sqrt{x}-2}{\sqrt{x}}\)

Answer 1

\(x>0;x\ne4\)

\(\left(\frac{1}{\sqrt{x}+2}+\frac{1}{\sqrt{x}-2}\right).\frac{\sqrt{x}-2}{\sqrt{x}}=\left(\frac{\sqrt{x}-2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}+\frac{\sqrt{x}+2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}\right)\frac{\sqrt{x}-2}{\sqrt{x}}\)

\(=\frac{2\sqrt{x}}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)}.\frac{\left(\sqrt{x}-2\right)}{\sqrt{x}}=\frac{2}{\sqrt{x}+2}\)