Question

rút gọn biểu thức : 

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

Answer 1

Đề nhầm à?

ĐK: \(x\ge0;x\ne1\)

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

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

Answer 2

Sửa đề: \(B=\dfrac{x+1-2\sqrt{x}}{\sqrt{x}-1}+\dfrac{x+\sqrt{x}}{\sqrt{x}+1}\)

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

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