Упр.941 ГДЗ Макарычев Миндюк 9 класс (Углубленный) (Алгебра)

а) (a-3a^(1/2))/(a+3a^(1/2));
б) (x^1,5-y^1,5)/(xy^0,5-x^0,5y);
в) (x^1,5+y^1,5)/(x^1,5-xy^0,5+x^0,5y);
г) (b-b^(1/3))/(b^(1/3)-1);
д) (c^0,6+d^0,9)/(c^0,2+d^0,3);
е) (a+b)/(a-a^(2/3)b^(1/3)+a^(1/3)b^(2/3)).

1. а)
   $$\frac{a-3a^{1/2}}{a+3a^{1/2}}=\frac{a^{1/2}(a^{1/2}-3)}{a^{1/2}(a^{1/2}+3)}=\frac{\sqrt a-3}{\sqrt a+3}.$$

2. б)
   $$\frac{x^{1,5}-y^{1,5}}{xy^{0,5}-x^{0,5}y}=\frac{(x^{0,5}-y^{0,5})(x+x^{0,5}y^{0,5}+y)}{x^{0,5}y^{0,5}(x^{0,5}-y^{0,5})}=\frac{x+\sqrt{xy}+y}{\sqrt{xy}}.$$

3. в)
   $$\frac{x^{1,5}+y^{1,5}}{x^{1,5}-xy^{0,5}+x^{0,5}y}=\frac{(x^{0,5}+y^{0,5})(x-x^{0,5}y^{0,5}+y)}{x^{0,5}(x-x^{0,5}y^{0,5}+y)}=\frac{\sqrt x+\sqrt y}{\sqrt x}.$$

4. г)
   $$\frac{b-b^{1/3}}{b^{1/3}-1}=\frac{b^{1/3}(b^{2/3}-1)}{b^{1/3}-1}=\frac{b^{1/3}(b^{1/3}-1)(b^{1/3}+1)}{b^{1/3}-1}=b^{2/3}+b^{1/3}.$$

5. д)
   $$\frac{c^{0,6}+d^{0,9}}{c^{0,2}+d^{0,3}}=\frac{(c^{0,2}+d^{0,3})(c^{0,4}-c^{0,2}d^{0,3}+d^{0,6})}{c^{0,2}+d^{0,3}}=c^{0,4}-c^{0,2}d^{0,3}+d^{0,6}.$$

6. е)
   $$\frac{a+b}{a-a^{2/3}b^{1/3}+a^{1/3}b^{2/3}}=\frac{(a^{1/3}+b^{1/3})(a^{2/3}-a^{1/3}b^{1/3}+b^{2/3})}{a^{1/3}(a^{2/3}-a^{1/3}b^{1/3}+b^{2/3})}=\frac{a^{1/3}+b^{1/3}}{a^{1/3}}.$$

Ответ

а) $$\frac{\sqrt a-3}{\sqrt a+3}$$; б) $$\frac{x+\sqrt{xy}+y}{\sqrt{xy}}$$; в) $$\frac{\sqrt x+\sqrt y}{\sqrt x}$$; г) $$b^{2/3}+b^{1/3}$$; д) $$c^{0,4}-c^{0,2}d^{0,3}+d^{0,6}$$; е) $$\frac{a^{1/3}+b^{1/3}}{a^{1/3}}$$.