Question

tìm điều kiện xác định .rút gọn

\(\left(\frac{\sqrt{x}}{x}-\frac{1}{2\sqrt{x}}\right):\left(\frac{x-\sqrt{x}}{\sqrt{x}+1}-\frac{x+\sqrt{x}}{\sqrt{x}-1}\right)\)

Answer 1

ĐKXĐ: \(x>0;x\ne1\)

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

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

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