Question

\(P=(\dfrac{x+2}{x\sqrt x-1} +\dfrac{\sqrt x}{x+\sqrt x+1}+\dfrac{1}{1-\sqrt x})÷ \dfrac{\sqrt x-1}{2}\)Rút gọn P

Chứg minh P>0

Answer 1

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

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

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

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

mình chỉ rút gọn thôi , bạn tự so sánh nha