Упр.103 Вариант 3 Дидактические материалы ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) (x^2-17)/(x+v17);
2) (vy-10)/(y-100);
3) (c+9vc)/(c-81);
4) (29+v29)/v29;
5) (a-10va+25)/(a-25);
6) (6-v12)/(v12-2).

1. $$\frac{x^2-17}{x+\sqrt{17}}=\frac{(x-\sqrt{17})(x+\sqrt{17})}{x+\sqrt{17}}=x-\sqrt{17}.$$
2. $$\frac{\sqrt{y}-10}{y-100}=\frac{\sqrt{y}-10}{(\sqrt{y}-10)(\sqrt{y}+10)}=\frac{1}{\sqrt{y}+10}.$$
3. $$\frac{c+9\sqrt{c}}{c-81}=\frac{\sqrt{c}(\sqrt{c}+9)}{(\sqrt{c}-9)(\sqrt{c}+9)}=\frac{\sqrt{c}}{\sqrt{c}-9}.$$
4. $$\frac{29+\sqrt{29}}{\sqrt{29}}=\frac{\sqrt{29}(\sqrt{29}+1)}{\sqrt{29}}=\sqrt{29}+1.$$
5. $$\frac{a-10\sqrt{a}+25}{a-25}=\frac{(\sqrt{a}-5)^2}{(\sqrt{a}-5)(\sqrt{a}+5)}=\frac{\sqrt{a}-5}{\sqrt{a}+5}.$$
6. $$\frac{6-\sqrt{12}}{\sqrt{12}-2}=\frac{\sqrt{6}(\sqrt{6}-\sqrt{2})}{\sqrt{2}(\sqrt{6}-\sqrt{2})}=\frac{\sqrt{6}}{\sqrt{2}}=\sqrt{3}.$$

Ответ

1) $$x-\sqrt{17}$$; 2) $$\frac{1}{\sqrt{y}+10}$$; 3) $$\frac{\sqrt{c}}{\sqrt{c}-9}$$; 4) $$\sqrt{29}+1$$; 5) $$\frac{\sqrt{a}-5}{\sqrt{a}+5}$$; 6) $$\sqrt{3}$$.