Question

Даю 25 баллов, 6.14 задание. Срочно!​

Answer 1

Ответ:

$\displaystyle \frac{a+2a^{1/3}}{a^{2/3}+2}=\frac{a^{1/3}\cdot (a^{2/3}+2)}{a^{2/3}+2}=a^{1/3}\\\\\\\frac{a-b^2}{a-a^{1/2}b}=\frac{(a^{1/2}-b)(a^{1/2}+b)}{a^{1/2}\, (a^{1/2}-b)}=\frac{a^{1/2}+b}{a^{1/2}}\\\\\\\frac{a^{0,5}-b^{0,5}}{a-b}=\frac{a^{0,5}-b^{0,5}}{(a^{0,5}-b^{0,5})(a^{0,5}+b^{0,5})}=\frac{1}{a^{0,5}+b^{0,5}}\\\\\\\frac{m^{5/4}n^{1/4}-m^{1/4}n^{5/4}}{m^{5/4}n^{5/4}}=\frac{m^{1/4}n^{1/4}\cdot (m-n)}{m^{5/4}n^{5/4}}=\frac{m-n}{mn}$

$\displaystyle \frac{a-b}{a^{2/3}+a^{1/3}b^{1/3}+b^{2/3}}=\frac{(a^{1/3}-b^{1/3})(a^{2/3}+a^{1/3}b^{1/3}+b^{2/3})}{a^{2/3}+a^{1/3}b^{1/3}+b^{2/3}}=a^{1/3}-b^{1/3}\\\\\\\frac{a-125}{a^{2/3}-25}=\frac{(a^{1/3}-5)(a^{2/3}+5a^{1/3}+25)}{(a^{1/3}-5)(a^{1/3}+5)}=\frac{a^{2/3}+5a^{1/3}+25}{a^{1/3}+5}$