Question

Rút gọn :

\(C=\frac{a+b}{\left(\sqrt{a}-\sqrt{b}\right)^2}-\frac{2}{\sqrt{ab}}:\left(\frac{1}{\sqrt{a}}-\frac{1}{\sqrt{b}}\right)^2\)

Answer 1

Lời giải:
ĐKXĐ:.............

\(C=\frac{a+b}{(\sqrt{a}-\sqrt{b})^2}-\frac{2}{\sqrt{ab}}:\left(\frac{\sqrt{b}-\sqrt{a}}{\sqrt{ab}}\right)^2=\frac{a+b}{(\sqrt{a}-\sqrt{b})^2}-\frac{2}{\sqrt{ab}}.\frac{ab}{(\sqrt{a}-\sqrt{b})^2}\)

\(=\frac{a+b}{(\sqrt{a}-\sqrt{b})^2}-\frac{2\sqrt{ab}}{(\sqrt{a}-\sqrt{b})^2}=\frac{a-2\sqrt{ab}+b}{(\sqrt{a}-\sqrt{b})^2}=\frac{(\sqrt{a}-\sqrt{b})^2}{(\sqrt{a}-\sqrt{b})^2}=1\)