Упр.248 Повторение ГДЗ Мерзляк 11 класс Базовый уровень (Алгебра)

1) (vx+1)/(x-1); 2) (a-3va)/(a-9);
3) (7-v7)/v7; 4) (v21+3)/(7+v21);
5) (m^(1/3)+n^(1/3))/(m+n);
6) (a^(1/4)-b^(1/4))/(va-vb);
7) (x^(1/3)-4)/(x^(1/6)-2);
8) (a+(a^3)^(1/4))/(va+a^(1/4).

1. $$\frac{\sqrt{x}+1}{x-1}=\frac{\sqrt{x}+1}{(\sqrt{x}-1)(\sqrt{x}+1)}=\frac{1}{\sqrt{x}-1}.$$
2. $$\frac{a-3\sqrt{a}}{a-9}=\frac{\sqrt{a}(\sqrt{a}-3)}{(\sqrt{a}-3)(\sqrt{a}+3)}=\frac{\sqrt{a}}{\sqrt{a}+3}.$$
3. $$\frac{7-\sqrt{7}}{\sqrt{7}}=\frac{\sqrt{7}(\sqrt{7}-1)}{\sqrt{7}}=\sqrt{7}-1.$$
4. $$\frac{\sqrt{21}+3}{7+\sqrt{21}}=\frac{\sqrt{3}(\sqrt{7}+\sqrt{3})}{\sqrt{7}(\sqrt{7}+\sqrt{3})}=\frac{\sqrt{3}}{\sqrt{7}}=\frac{\sqrt{21}}{7}.$$
5. $$\frac{\sqrt[3]{m}+\sqrt[3]{n}}{m+n}=\frac{1}{\sqrt[3]{m^2}-\sqrt[3]{mn}+\sqrt[3]{n^2}}.$$
6. $$\frac{\sqrt[4]{a}-\sqrt[4]{b}}{\sqrt{a}-\sqrt{b}}=\frac{\sqrt[4]{a}-\sqrt[4]{b}}{(\sqrt[4]{a}-\sqrt[4]{b})(\sqrt[4]{a}+\sqrt[4]{b})}=\frac{1}{\sqrt[4]{a}+\sqrt[4]{b}}.$$
7. $$\frac{\sqrt[3]{x}-4}{\sqrt[6]{x}-2}=\frac{(\sqrt[6]{x})^2-4}{\sqrt[6]{x}-2}=\frac{(\sqrt[6]{x}-2)(\sqrt[6]{x}+2)}{\sqrt[6]{x}-2}=\sqrt[6]{x}+2.$$
8. $$\frac{a+\sqrt[4]{a^3}}{\sqrt{a}+\sqrt[4]{a}}=\frac{\sqrt[4]{a^3}(\sqrt[4]{a}+1)}{\sqrt[4]{a}(\sqrt[4]{a}+1)}=\sqrt[4]{a^2}=\sqrt{a}.$$

Ответ

1) $$\frac{1}{\sqrt{x}-1}$$; 2) $$\frac{\sqrt{a}}{\sqrt{a}+3}$$; 3) $$\sqrt{7}-1$$; 4) $$\frac{\sqrt{21}}{7}$$; 5) $$\frac{1}{\sqrt[3]{m^2}-\sqrt[3]{mn}+\sqrt[3]{n^2}}$$; 6) $$\frac{1}{\sqrt[4]{a}+\sqrt[4]{b}}$$; 7) $$\sqrt[6]{x}+2$$; 8) $$\sqrt{a}$$.