Question

[Việt Hoàng]

Rút gọn biểu thức sau: a) 1-x√x /1-√x + √x ( x lớn hơn hoặc bằng 0 , x khác 1)

Answer 1

[Nguyễn Lê Phước Thịnh]

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

Answer 2

[Nguyễn Ngọc Huy Toàn]

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

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

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

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

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