Question

7. Упростите выражение: VX x-y ( - , x >0, y >0, x≠ y. x²+xy √x - √ √x + √​

Answer 1

Ответ:

$\displaystyle \frac{1}{x}$

Объяснение:

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

$\displaystyle (\frac{\sqrt{x}(\sqrt{x}+\sqrt{y})}{(\sqrt x- \sqrt y)(\sqrt x + \sqrt y)}-\frac{\sqrt{y}(\sqrt{x}-\sqrt{y})}{(\sqrt x- \sqrt y)(\sqrt x + \sqrt y)})\cdot \frac{x-y}{x(x+y)}=$

$\displaystyle \\\\(\frac{x+\sqrt{xy})}{x-y}-\frac{\sqrt{xy}-y)}{x-y})\cdot \frac{x-y}{x(x+y)}=$

$\displaystyle \frac{x+\sqrt{xy}-(\sqrt{xy}-y)}{x-y}\cdot \frac{x-y}{x(x+y)}=\\\\\frac{x+\sqrt{xy}-\sqrt{xy}+y}{x-y}\cdot \frac{x-y}{x(x+y)}=\\\\\frac{x+y}{x-y}\cdot \frac{x-y}{x(x+y)}=\frac{1}{x}$