Question

9．已知x=$\sqrt{2}-1$，y=$\sqrt{2}+1$，求$\frac{{x}^{2}-2xy+{y}^{2}}{{x}^{2}-{y}^{2}}$的值．

Answer 1

分析 首先将分式因式分解进而将已知代入求出即可．

解答 解：∵x=$\sqrt{2}-1$，y=$\sqrt{2}+1$，
∴$\frac{{x}^{2}-2xy+{y}^{2}}{{x}^{2}-{y}^{2}}$
=$\frac{（x-y）^{2}}{（x+y）（x-y）}$
=$\frac{x-y}{x+y}$
=$\frac{\sqrt{2}-1-\sqrt{2}-1}{\sqrt{2}-1+\sqrt{2}+1}$
=$\frac{-2}{2\sqrt{2}}$
=-$\frac{\sqrt{2}}{2}$．

点评 此题主要考查了二次根式的化简求值，正确分解因式得出是解题关键．