Question

Answer 1

Lời giải:
Gọi biểu thức trên là $A$

\(A=\left[\frac{\sqrt{x}-2}{(\sqrt{x}-1)^2}+\frac{2+\sqrt{x}}{x-1}\right].\frac{x-1}{x-2}\)

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

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

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