Question

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

Rút gọn biểu thức P

Answer 1

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

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

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

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

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

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

\(P=2\)

vậy  \(P=2\)