Упражнение 150

\({\largeа)}\ \left(\frac{x}{y^2}-\frac{1}{x}\right):\left(\frac{1}{y}+\frac{1}{x}\right)=\frac{x^2-y^2}{xy^2}:\frac{x+y}{xy}=\frac{x^2-y^2}{xy^2}\cdot\frac{xy}{x+y}=\frac{ (x-y)(x+y)\cdot{xy}}{xy^2\cdot(x+y)}=\frac{x-y}{y};\)

\({\largeб)}\ \left(\frac{a}{m^2}+\frac{a^2}{m^3}\right):\left(\frac{m^2}{a^2}+\frac{m}{a}\right)=\frac{am+a^2}{m^3}:\frac{m^2+am}{a^2}=\frac{am+a^2}{m^3}\cdot\frac{a^2}{m^2+am}=\frac{ a(m+a)\cdot{a^2}}{m^3\cdot{m}(m+a)}=\frac{a^3}{m^4};\)

\({\largeв)}\ \frac{ab+b^2}{3}:\frac{b^3}{3a}+\frac{a+b}{b}=\frac{ab+b^2}{3}\cdot\frac{3a}{b^3}+\frac{a+b}{b}=\frac{ b(a+b)\cdot3a}{3\cdot{b^3}}+\frac{a+b}{b}=\frac{ a(a+b)}{b^2}+\frac{a+b}{b}=\frac{ a(a+b)+b(a+b)}{b^2}=\frac{ (a+b)(a+b)}{b^2}=\frac{ (a+b)^2}{b^2};\)

\({\largeг)}\ \frac{x-y}{x}-\frac{5y}{x^2}\cdot\frac{x^2-xy}{5y}=\frac{x-y}{x}-\frac{5y\cdot{x}(x-y)}{x^2\cdot5y}=\frac{x-y}{x}-\frac{x-y}{x}=0.\)