Question

Rút gọn biểu thức

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

Answer 1

Ta có: \(P=\frac{1}{x^2-\sqrt{x}}:\frac{\sqrt{x}+1}{\sqrt{x}+x+x\sqrt{x}}\)

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

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

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