Question

[Thắm Nguyễn Thị]

Rút gọn:

\(\frac{x}{\sqrt{x}-1}-\frac{1}{\sqrt{x}+1}+\frac{\sqrt{x}-1}{x-1}\) 

Answer 1

[Nguyễn Tấn Phát]

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