Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 506

а) $$ \left(\frac{1}{x+x \sqrt{y}}+\frac{1}{x-x \sqrt{y}}\right) $$ ⋅ y − 1/2
1) $$ \frac{1}{x+x \sqrt{y}}+\frac{1}{x-x \sqrt{y}}=\frac{1(x-x \sqrt{y})}{(x+x \sqrt{y})(x-x \sqrt{y})}+ $$ $$ \frac{1(x+x \sqrt{y})}{(x-x \sqrt{y})(x+x \sqrt{y})}=\frac{x-x \sqrt{y}+x+x \sqrt{y}}{x^2-(x \sqrt{y})^2} $$ = 2x/x² − x²y = 2x/x²(1 − y) = 2x : x/x²(1 − y) : x = 2x/x(1 − y)
2) 2x/x(1 − y) ⋅ y − 1/2 = 2 ⋅ (−(1 − y))/x(1 − y) ⋅ 2 = −2 ⋅ (1 − y) : 2(1 − y)/x(1 − y) ⋅ 2 : 2(1 − y) = −1/x
б) $$ \left(\frac{\sqrt{a}}{\sqrt{a}-\sqrt{b}}-\frac{\sqrt{a}}{\sqrt{a}+\sqrt{b}}\right) $$ ⋅ (b − a)²/2
1) $$ \frac{\sqrt{a}}{\sqrt{a}-\sqrt{b}}-\frac{\sqrt{a}}{\sqrt{a}+\sqrt{b}}=\frac{\sqrt{a}(\sqrt{a}+\sqrt{b})}{(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b})}-\frac{\sqrt{a}(\sqrt{a}-\sqrt{b})}{(\sqrt{a}+\sqrt{b})(\sqrt{a}-\sqrt{b})}= $$ $$ \frac{\sqrt{a} \boxminus \sqrt{a}+\sqrt{a} \cdot \sqrt{b}-\sqrt{a} \cdot \sqrt{a}+\sqrt{a} \cdot \sqrt{b}}{(\sqrt{a})^2-(\sqrt{b})^2}=\frac{a+\sqrt{a b}-a+\sqrt{a b}}{a-b}=\frac{2 \sqrt{a b}}{a-b} $$
2) $$ \frac{2 \sqrt{a b}}{a-b} $$ ⋅ (b − a)²/2 = $$ \frac{2 \sqrt{a b}(a-b)^2}{(a-b) 2}=\frac{2 \sqrt{a b}(a-b)^2 \div 2(a-b)}{(a-b) 2 \div 2(a-b)}=\frac{\sqrt{a b}(a-b)}{1} $$ = $$\sqrt{ab}$$(a − b)