656 Вправа 656Алгебра 8 клас Тарасенкова 2025 · § 15 · стор. 194

656. Спростіть вираз:

1) ${\displaystyle \frac{{\sqrt{n}-2}^{\mathrm{\setminus }\left(\sqrt{n}-2\right)}}{\sqrt{n}+2}-\frac{{\sqrt{n}+2}^{\mathrm{\setminus }\left(\sqrt{n}+2\right)}}{\sqrt{n}-2}=}$${\displaystyle \frac{{(\sqrt{n}-2)}^2-{(\sqrt{n}+2)}^2}{{\left(\sqrt{n}\right)}^2-2^2}=}$${\displaystyle \frac{(n-4\sqrt{n}+4)-(n+4\sqrt{n}+4)}{n-4}=}$${\displaystyle \frac{n-4\sqrt{n}+4-n-4\sqrt{n}-4}{n-4}=}$${\displaystyle \frac{-8\sqrt{n}}{n-4}=}$${\displaystyle \frac{8\sqrt{n}}{4-n}}$;

2) ${\displaystyle \frac{\sqrt{x}+\sqrt{y}}{\sqrt{y}-\sqrt{x}}+\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}=}$${\displaystyle \frac{-(\sqrt{x}+\sqrt{y})}{\sqrt{x}-\sqrt{y}}+\frac{\sqrt{x}-\sqrt{y}}{\sqrt{x}+\sqrt{y}}=}$${\displaystyle \frac{-{(\sqrt{x}+\sqrt{y})}^2+{(\sqrt{x}-\sqrt{y})}^2}{x-y}=}$${\displaystyle \frac{-(x+2\sqrt{xy}+y)+(x-2\sqrt{xy}+y)}{x-y}=}$${\displaystyle \frac{-x-2\sqrt{xy}-y+x-2\sqrt{xy}+y}{x-y}=}$${\displaystyle \frac{-4\sqrt{xy}}{x-y}=}$${\displaystyle \frac{4\sqrt{xy}}{y-x}}$.