Question

Выражения: (a/m^2+a^2/m^3): (m^2/a^2+m/a); ab+b^2/3: b^3/3a+a+b/b; x-y/x-5y/x^2*x^2-xy/5y

Answer 1

$( \frac{a}{m^2} + \frac{a^2}{m^3}):( \frac{m^2}{a^2}+ \frac{m}{a} ) = \frac{am^3+a^2m^2}{m^5} : \frac{am^2+a^2m}{a^3} = \frac{am^3+a^2m^2}{m^5}* \frac{a^3}{am^2+a^2m} \\ = \frac{am^2(m+a)}{m^5}* \frac{a^3}{am(m+a)} =\frac{ma^3}{m^5}=\frac{a^3}{m^4}$

$\frac{ab+b^2}{3} : \frac{b^3}{3a}+ \frac{a+b}{b}=\frac{ab+b^2}{3}*\frac{3a}{b^3}+ \frac{a+b}{b}= \\ =\frac{a(ab+b^2)}{b^3}+ \frac{a+b}{b}=\frac{ab(a+b)}{b^3}+ \frac{a+b}{b}=\frac{a(a+b)}{b^2}+ \frac{a+b}{b}=\frac{a(a+b)+b(a+b)}{b^2}= \\ =\frac{(a+b)(a+b)}{b^2}=\frac{(a+b)^2}{b^2}$

$\frac{x-y}{x} - \frac{5y}{ x^{2} } * \frac{x^2-xy}{5y}$