Question

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

Answer 1

P=\(\left(\frac{1}{\sqrt{x}-1}-\frac{1}{x+\sqrt{x}}\right):\frac{x-\sqrt{x}+1}{x\sqrt{x}+1}\)(đk:\(x\ge0;x\ne1\))

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

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

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

vậy P=\(\frac{x+1}{x-\sqrt{x}}\) với \(x\ge0;x\ne1\)

Answer 2

https://i.imgur.com/g9DzyxW.jpg