Question

СРОЧНО АЛГЕБРА 8 КЛАСС

Answer 1

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

$2)\frac{x\sqrt{y}-y\sqrt{y}}{2}*\frac{2x}{(\sqrt{x}+\sqrt{y})(\sqrt{x}-\sqrt{y})}=\frac{\sqrt{y}(x-y)}{2}*\frac{2x}{(\sqrt{x})^{2}-(\sqrt{y})^{2}}=\sqrt{y}(x-y)*\frac{x}{x-y}=x\sqrt{y}\\\\Otvet:\boxed{x\sqrt{y}}$