Question

Answer 1

Lời giải:

a.

\(P=\left[\frac{x+2\sqrt{x}-7}{(\sqrt{x}-3)(\sqrt{x}+3)}-\frac{(\sqrt{x}-1)(\sqrt{x}+3)}{(\sqrt{x}-3)(\sqrt{x}+3)}\right]:\frac{\sqrt{x}-1-\sqrt{x}-3}{(\sqrt{x}+3)(\sqrt{x}-1)}\)

\(=\frac{x+2\sqrt{x}-7-(x+2\sqrt{x}-3)}{(\sqrt{x}-3)(\sqrt{x}+3)}:\frac{-4}{(\sqrt{x}+3)(\sqrt{x}-1)}=\frac{-4}{(\sqrt{x}-3)(\sqrt{x}+3)}.\frac{(\sqrt{x}+3)(\sqrt{x}-1)}{-4}=\frac{\sqrt{x}-1}{\sqrt{x}-3}\)

b. Khi $x=4-2\sqrt{3}=(\sqrt{3}-1)^2\Rightarrow \sqrt{x}=\sqrt{3}-1$

$P=\frac{\sqrt{3}-1-1}{\sqrt{3}-1-3}=\frac{5-2\sqrt{3}}{13}$