Question

[Aki Yoko]

A = \(\dfrac{\sqrt{x}-1}{\sqrt{x}}\)

B = \(\dfrac{\sqrt{x}-1}{\sqrt{x}}+\dfrac{1-\sqrt{x}}{x+\sqrt{x}}\)

Tính P = \(\dfrac{A}{B}\)

Answer 1

[Nguyễn Lê Phước Thịnh]

Ta có: \(P=\dfrac{A}{B}\)

\(\Leftrightarrow P=\dfrac{\sqrt{x}-1}{\sqrt{x}}:\left(\dfrac{\sqrt{x}-1}{\sqrt{x}}+\dfrac{1-\sqrt{x}}{x+\sqrt{x}}\right)\)

\(\Leftrightarrow P=\dfrac{\sqrt{x}-1}{\sqrt{x}}:\left(\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}+1\right)}+\dfrac{1-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+1\right)}\right)\)

\(\Leftrightarrow P=\dfrac{\sqrt{x}-1}{\sqrt{x}}:\left(\dfrac{x-1+1-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+1\right)}\right)\)

\(\Leftrightarrow P=\dfrac{\sqrt{x}-1}{\sqrt{x}}:\dfrac{x-\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+1\right)}\)

\(\Leftrightarrow P=\dfrac{\sqrt{x}-1}{\sqrt{x}}\cdot\dfrac{\sqrt{x}\left(\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}\)

\(\Leftrightarrow P=\dfrac{\sqrt{x}+1}{\sqrt{x}}\)

Answer 2

[Nguyễn Công Tỉnh]