Упр.103 Вариант 1 Дидактические материалы ГДЗ Мерзляк Полонский 8 класс (Алгебра)

1) (x^2-11)/(x+v11);
2) (vx-12)/(x-144);
3) (a+3va)/(a-9);
4) (17-v17)/v17;
5) (m-12vm+36)/(m-36);
6) (v21-3)/(7-v21).

1. $$\frac{x^2-11}{x+\sqrt{11}}=\frac{(x-\sqrt{11})(x+\sqrt{11})}{x+\sqrt{11}}=x-\sqrt{11}.$$

2. $$\frac{\sqrt{x}-12}{x-144}=\frac{\sqrt{x}-12}{(\sqrt{x}-12)(\sqrt{x}+12)}=\frac{1}{\sqrt{x}+12}.$$

3. $$\frac{a+3\sqrt{a}}{a-9}=\frac{\sqrt{a}(\sqrt{a}+3)}{(\sqrt{a}-3)(\sqrt{a}+3)}=\frac{\sqrt{a}}{\sqrt{a}-3}.$$

4. $$\frac{17-\sqrt{17}}{\sqrt{17}}=\frac{\sqrt{17}(\sqrt{17}-1)}{\sqrt{17}}=\sqrt{17}-1.$$

5. $$\frac{m-12\sqrt{m}+36}{m-36}=\frac{(\sqrt{m}-6)^2}{(\sqrt{m}-6)(\sqrt{m}+6)}=\frac{\sqrt{m}-6}{\sqrt{m}+6}.$$

6. $$\frac{\sqrt{21}-3}{7-\sqrt{21}}=\frac{\sqrt{3}\sqrt{7}-\sqrt{3}\sqrt{3}}{\sqrt{7}\sqrt{7}-\sqrt{3}\sqrt{7}}=\frac{\sqrt{3}(\sqrt{7}-\sqrt{3})}{\sqrt{7}(\sqrt{7}-\sqrt{3})}=\frac{\sqrt{3}}{\sqrt{7}}=\sqrt{\frac{3}{7}}.$$

Ответ

1) $$x-\sqrt{11}$$; 2) $$\frac{1}{\sqrt{x}+12}$$; 3) $$\frac{\sqrt{a}}{\sqrt{a}-3}$$; 4) $$\sqrt{17}-1$$; 5) $$\frac{\sqrt{m}-6}{\sqrt{m}+6}$$; 6) $$\sqrt{\frac{3}{7}}$$.