Question

Rút gọn biểu thức

C=\(\dfrac{x+y+2\sqrt{xy}}{\sqrt{x}+\sqrt{y}}:\dfrac{1}{\sqrt{x}-\sqrt{y}}\)             (x>0; y>0; y≠0)

P=\(\left(\dfrac{2}{x-\sqrt{x}}+\dfrac{\sqrt{x}+1}{\sqrt{x}}-\dfrac{\sqrt{x}+1}{\sqrt{x}-1}\right):\dfrac{\sqrt{x}+1}{2\sqrt{x}-x}\)            

D=\(\left(\dfrac{1}{\sqrt{a}+2}+\dfrac{1}{\sqrt{a}-2}\right):\dfrac{\sqrt{a}}{a-4}\)       (a>0; a≠0)

Answer 1

a: \(=\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)=x-y\)

b: \(=\dfrac{2+x-1-x-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-1\right)}\cdot\dfrac{\sqrt{x}\left(2-\sqrt{x}\right)}{\sqrt{x}+1}\)

\(=\dfrac{1-\sqrt{x}}{\sqrt{x}-1}\cdot\dfrac{1}{\sqrt{x}+1}=-\dfrac{1}{\sqrt{x}+1}\)

c: \(=\dfrac{\sqrt{a}-2+\sqrt{a}+2}{a-4}\cdot\dfrac{a-4}{\sqrt{a}}=2\)