Упр.28.188 ГДЗ Мерзляк 11 класс Углубленный уровень (Алгебра)
- Сократите дробь:
1) $$\frac{x-8x^{\frac{3}{7}}}{x^{\frac{4}{7}}-8}$$;
4) $$\frac{m^{1{,}5}-n^{1{,}5}}{m+m^{0{,}5}n^{0{,}5}+n}$$;
7) $$\frac{x^{\frac{5}{8}}+6x^{\frac{1}{4}}}{x-36x^{\frac{1}{4}}}$$;
2) $$\frac{5y^{\frac{2}{3}}}{y^{\frac{5}{6}}+y^{\frac{2}{3}}}$$;
5) $$\frac{a-2a^{0{,}5}b^{0{,}5}+b}{ab^{0{,}5}-a^{0{,}5}b}$$;
8) $$\frac{26^{\frac{1}{5}}+2^{\frac{1}{5}}}{52^{\frac{1}{5}}+4^{\frac{1}{5}}}$$;
3) $$\frac{a^{0{,}5}+b^{0{,}5}}{a-b}$$;
6) $$\frac{8a+1}{4a^{\frac{2}{3}}-1}$$.
$$\frac{x-8x^{3/7}}{x^{4/7}-8}=\frac{x^{3/7}\left(x^{4/7}-8\right)}{x^{4/7}-8}=x^{3/7}.$$
$$\frac{5y^{2/3}}{y^{5/6}+y^{2/3}}=\frac{5y^{2/3}}{y^{2/3}\left(y^{1/6}+1\right)}=\frac{5}{y^{1/6}+1}.$$
$$\frac{a^{0.5}+b^{0.5}}{a-b}=\frac{a^{0.5}+b^{0.5}}{\left(a^{0.5}-b^{0.5}\right)\left(a^{0.5}+b^{0.5}\right)}=\frac{1}{\sqrt{a}-\sqrt{b}}.$$
$$\frac{m^{1.5}-n^{1.5}}{m+m^{0.5}n^{0.5}+n}=\frac{\left(m^{0.5}-n^{0.5}\right)\left(m+m^{0.5}n^{0.5}+n\right)}{m+m^{0.5}n^{0.5}+n}=\sqrt{m}-\sqrt{n}.$$
$$\frac{a-2a^{0.5}b^{0.5}+b}{ab^{0.5}-a^{0.5}b}=\frac{\left(a^{0.5}-b^{0.5}\right)^2}{a^{0.5}b^{0.5}\left(a^{0.5}-b^{0.5}\right)}=\frac{\sqrt{a}-\sqrt{b}}{\sqrt{ab}}.$$
$$\frac{8a+1}{4a^{2/3}-1}=\frac{\left(2a^{1/3}+1\right)\left(4a^{2/3}-2a^{1/3}+1\right)}{\left(2a^{1/3}+1\right)\left(2a^{1/3}-1\right)}=\frac{4a^{2/3}-2a^{1/3}+1}{2a^{1/3}-1}.$$
$$\frac{x^{5/8}+6x^{1/4}}{x-36x^{1/4}}=\frac{x^{1/4}\left(x^{3/8}+6\right)}{x^{1/4}\left(x^{3/4}-36\right)}=\frac{x^{3/8}+6}{\left(x^{3/8}+6\right)\left(x^{3/8}-6\right)}=\frac{1}{x^{3/8}-6}.$$
$$\frac{26^{1/5}+2^{1/5}}{52^{1/5}+4^{1/5}}=\frac{26^{1/5}+2^{1/5}}{2^{1/5}\left(26^{1/5}+2^{1/5}\right)}=\frac{1}{2^{1/5}}=2^{-1/5}.$$
Ответ
1) $$x^{3/7}$$; 2) $$\frac{5}{y^{1/6}+1}$$; 3) $$\frac{1}{\sqrt{a}-\sqrt{b}}$$; 4) $$\sqrt{m}-\sqrt{n}$$; 5) $$\frac{\sqrt{a}-\sqrt{b}}{\sqrt{ab}}$$; 6) $$\frac{4a^{2/3}-2a^{1/3}+1}{2a^{1/3}-1}$$; 7) $$\frac{1}{x^{3/8}-6}$$; 8) $$2^{-1/5}$$.
