Question

[dfgh]

2Cho biểu thức

 (với x > 0; x ¹ 1)

                    a)  Rút gọn biểu thức A.

GIÚP TỚ VỚI Ạ PLSSSS

Answer 1

[HT.Phong (9A5)]

\(A=\left(\dfrac{1}{x+2\sqrt{x}}-\dfrac{1}{\sqrt{x}+2}\right):\dfrac{1-\sqrt{x}}{x+4\sqrt{x}+4}\left(x>0;x\ne1\right)\)

\(A=\left[\dfrac{1}{\sqrt{x}\left(\sqrt{x}+2\right)}-\dfrac{\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+2\right)}\right]:\dfrac{1-\sqrt{x}}{\left(\sqrt{x}\right)^2+2\cdot\sqrt{x}\cdot2+2^2}\)

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

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

\(A=\dfrac{\left(\sqrt{x}+2\right)^2}{\sqrt{x}\left(\sqrt{x}+2\right)}\)

\(A=\dfrac{\sqrt{x}+2}{\sqrt{x}}\)

Vậy: ...