Question

Cho biểu thức \(A=\left(\frac{\sqrt{x}+1}{\sqrt{x}-1}-\frac{\sqrt{x}-1}{\sqrt{x}+1}-\frac{\sqrt[]{x}}{x-1}\right):\frac{4\sqrt{x}-8}{1-x}\)

Rút gọn

Answer 1

\(DK:\left\{{}\begin{matrix}x\ne\pm1\\x\ne4\end{matrix}\right.\)

\(A=\left(\frac{\sqrt{x}+1}{\sqrt{x}-1}-\frac{\sqrt{x}-1}{\sqrt{x}+1}-\frac{\sqrt{x}}{x-1}\right):\frac{4\sqrt{x}-8}{1-x}\)

\(=\left[\frac{\left(\sqrt{x}+1\right)^2-\left(\sqrt{x}-1\right)^2-\sqrt{x}}{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}\right].\frac{x-1}{8-4\sqrt{x}}\)

\(=\frac{4\sqrt{x}}{x-1}.\frac{x-1}{8-4\sqrt{x}}=\frac{4\sqrt{x}}{8-4\sqrt{x}}\)