Question

Rút gọn M= \(\left(\dfrac{\sqrt{a}}{9}-\dfrac{1}{\sqrt{a}}\right)^2\left(\dfrac{\sqrt{a}-3}{\sqrt{a}+3}-\dfrac{\sqrt{a}+3}{\sqrt{a}-3}\right)\)

Answer 1

điều kiện xác định : \(a>0;a\ne9\)

ta có : \(M=\left(\dfrac{\sqrt{a}}{9}-\dfrac{1}{\sqrt{a}}\right)^2\left(\dfrac{\sqrt{a}-3}{\sqrt{a}+3}-\dfrac{\sqrt{a}+3}{\sqrt{a}-3}\right)\)

\(\Leftrightarrow M=\left(\dfrac{a-9}{9\sqrt{a}}\right)^2\left(\dfrac{\left(\sqrt{a}-3\right)^2-\left(\sqrt{a}+3\right)^2}{\left(\sqrt{a}+3\right)\left(\sqrt{a}-3\right)}\right)\)

\(\Leftrightarrow M=\left(\dfrac{a-9}{9\sqrt{a}}\right)^2\left(\dfrac{-12\sqrt{a}}{a-9}\right)=\dfrac{-4\left(a-9\right)}{27\sqrt{a}}\)