Question

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

a. Tìm điều kiện của x để A có nghĩa

b. Rút gọn A

Answer 1

a) ĐKXĐ: x≠0;x≠1;x>0

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