Question

Cho biểu thức

a) Rút gọn P

b) Tìm các giá trị của x để P > 0

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

Answer 1

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

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

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

Có P > 0 => \(\frac{x-1}{\sqrt{x}}>0\)

Vì \(x>0\) => x - 1 > 0 => x > 1