Question

rút gọn biểu thức

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

Answer 1

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

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

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

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

\(=\frac{2x+2\sqrt{x}+2}{\sqrt{x}}\)