Question

(\(\dfrac{a}{\sqrt{ab}+a}+\dfrac{b}{\sqrt{ab}-b}\)):\(\left(\dfrac{ab}{a-b}\right)\)

rút gọn P

Answer 1

\(\left(\dfrac{a}{\sqrt{ab}+a}+\dfrac{b}{\sqrt{ab}-b}\right):\dfrac{ab}{a-b}=\left[\dfrac{a}{\sqrt{a}\left(\sqrt{a}+\sqrt{b}\right)}+\dfrac{b}{\sqrt{b}\left(\sqrt{a}-\sqrt{b}\right)}\right]:\dfrac{ab}{a-b}=\left(\dfrac{\sqrt{a}}{\sqrt{a}+\sqrt{b}}+\dfrac{\sqrt{b}}{\sqrt{a}-\sqrt{b}}\right).\dfrac{a-b}{ab}=\dfrac{\sqrt{a}\left(\sqrt{a}-\sqrt{b}\right)+\sqrt{b}\left(\sqrt{a}+\sqrt{b}\right)}{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}.\dfrac{a-b}{ab}=\dfrac{a-\sqrt{ab}+\sqrt{ab}+b}{a-b}.\dfrac{a-b}{ab}=\dfrac{a+b}{ab}\)

Answer 2

ĐKXĐ: \(ab>0;a\ne b\)