Упр.17.17 ГДЗ Мерзляк Поляков 8 класс (Алгебра)

1) (x-25)/(vx-5); 2) (va+2)/(a-4);
3) (a-3)/(va+v3); 4) (v10+v5)/v5;
5) (23-v23)/v23; 6) (v24-v28)/(v54-v63);
7) (va-vb)/(a-2vab+b); 8) (b-8vb+16)/(vb-4).

1. $$\frac{x-25}{\sqrt{x}-5}=\frac{(\sqrt{x}-5)(\sqrt{x}+5)}{\sqrt{x}-5}=\sqrt{x}+5.$$
2. $$\frac{\sqrt{a}+2}{a-4}=\frac{\sqrt{a}+2}{(\sqrt{a}-2)(\sqrt{a}+2)}=\frac{1}{\sqrt{a}-2}.$$
3. $$\frac{a-3}{\sqrt{a}+\sqrt{3}}=\frac{(\sqrt{a}-\sqrt{3})(\sqrt{a}+\sqrt{3})}{\sqrt{a}+\sqrt{3}}=\sqrt{a}-\sqrt{3}.$$
4. $$\frac{\sqrt{10}+\sqrt{5}}{\sqrt{5}}=\frac{\sqrt{5}\sqrt{2}+\sqrt{5}}{\sqrt{5}}=\frac{\sqrt{5}(\sqrt{2}+1)}{\sqrt{5}}=\sqrt{2}+1.$$
5. $$\frac{23-\sqrt{23}}{\sqrt{23}}=\frac{\sqrt{23}(\sqrt{23}-1)}{\sqrt{23}}=\sqrt{23}-1.$$
6. $$\frac{\sqrt{24}-\sqrt{28}}{\sqrt{54}-\sqrt{63}}=\frac{\sqrt{6\cdot 4}-\sqrt{7\cdot 4}}{\sqrt{9\cdot 6}-\sqrt{9\cdot 7}}=\frac{\sqrt{4}(\sqrt{6}-\sqrt{7})}{\sqrt{9}(\sqrt{6}-\sqrt{7})}=\frac{2}{3}.$$
7. $$\frac{\sqrt{a}-\sqrt{b}}{a-2\sqrt{ab}+b}=\frac{\sqrt{a}-\sqrt{b}}{(\sqrt{a}-\sqrt{b})^2}=\frac{1}{\sqrt{a}-\sqrt{b}}.$$
8. $$\frac{b-8\sqrt{b}+16}{\sqrt{b}-4}=\frac{(\sqrt{b}-4)^2}{\sqrt{b}-4}=\sqrt{b}-4.$$

Ответ

1) $$\sqrt{x}+5$$; 2) $$\frac{1}{\sqrt{a}-2}$$; 3) $$\sqrt{a}-\sqrt{3}$$; 4) $$\sqrt{2}+1$$; 5) $$\sqrt{23}-1$$; 6) $$\frac{2}{3}$$; 7) $$\frac{1}{\sqrt{a}-\sqrt{b}}$$; 8) $$\sqrt{b}-4$$.