Question

Cho biểu thức: G= (x-\(\sqrt{x}\)+2/x-1 -1/\(\sqrt{x}\)-1)* x+2\(\sqrt{x}\)+1/2x-2\(\sqrt{x}\) ( với x>0; x≠1)

rút gon G

Answer 1

Ta có: \(G=\left(\dfrac{x-\sqrt{x}+2}{x-1}-\dfrac{1}{\sqrt{x}-1}\right)\cdot\dfrac{x+2\sqrt{x}+1}{2x-2\sqrt{x}}\)

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

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

\(=\dfrac{\sqrt{x}+1}{2\sqrt{x}}\)