Question

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

1. Rút gọn biểu thức

2. tìm GTNN của P

giúp mình với :(( đang gấp

Answer 1

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

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

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

\(=\frac{x\sqrt{x}+x-\sqrt{x}+3}{\sqrt{x}+1}.x\)

\(=\frac{x^2\sqrt{x}+x^2-x\sqrt{x}+3x}{\sqrt{x}+1}\)

\(........?!\)