ПОВТОРЮЄМО АЛГЕБРУ ЗА 8 КЛАС: 50

50. Скоротіть дріб:

1) $\frac{y-36}{y-6\sqrt{y}}$ = $\frac{(\sqrt{y}-6)(\sqrt{y}+6)}{\sqrt{y}(\sqrt{y}-6)}$ = $\frac{\sqrt{y}+6}{\sqrt{y}}$;

2) $\frac{a-6\sqrt{a}\sqrt{b}+9b}{a-9b}$ = $\frac{{(\sqrt{a}-3\sqrt{b})}^2}{(\sqrt{a}-3\sqrt{b})(\sqrt{a}+3\sqrt{b})}$ = $\frac{\sqrt{a}-3\sqrt{b}}{\sqrt{a}+3\sqrt{b}}$;

3) $\frac{\sqrt{26}+13}{2+\sqrt{26}}$ = $\frac{{\sqrt{2}•\sqrt{13}+\left(\sqrt{13}\right)}^2}{{\left(\sqrt{2}\right)}^2+\sqrt{2}•\sqrt{13}}$ = $\frac{\sqrt{13}(\sqrt{2}+\sqrt{13})}{\sqrt{2}(\sqrt{2}+\sqrt{13})}$ = $\sqrt{\frac{13}{2}}$ = $\sqrt{\mathrm{6,5}}$.