Question

Cho A=(1/(1+√x) -1/(√x-1)):(1/(1-√x) -1/(√x+1))+1/1-√x

a/Rút gọn A

b/Tính A với x=7-4√3

c/Tìm x để A=-1/2

Giúp mk với nha. Đang cần gấp ạ.

Answer 1

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

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

\(=\dfrac{-2}{x-1}\cdot\dfrac{1-x}{2\sqrt{x}}+\dfrac{1}{1-\sqrt{x}}\)

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

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

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

b) thay \(x=7-4\sqrt{3}\) vào A, ta được:

\(A=\dfrac{1}{\sqrt{7-4\sqrt{3}}-\left(7-4\sqrt{3}\right)}=\dfrac{1}{2-\sqrt{3}-7+4\sqrt{3}}=\dfrac{1}{3\sqrt{3}-5}\)

c) Đk: x > 0, x khác 1

\(A=-\dfrac{1}{2}\) \(\Leftrightarrow\dfrac{1}{\sqrt{x}-x}=-\dfrac{1}{2}\Leftrightarrow\sqrt{x}-x=-2\)

\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=2\\\sqrt{x}=-1\left(vn\right)\end{matrix}\right.\) \(\Leftrightarrow x=4\) (N)

Kl:........