Упражнение 121

\({\largeа)}\ \frac{x^2-xy}{y}\cdot\frac{y^2}{x}=\frac{ x(x-y)\cdot{y^2}}{y\cdot{x}}=y(x-y)=xy-y^2;\)

\({\largeб)}\ \frac{3a}{b^2}\cdot\frac{ab+b^2}{9}=\frac{3a\cdot{b}(a+b)}{b^2\cdot9}=\frac{ a(a+b)}{3b}=\frac{a^2+ab}{3b};\)

\({\largeв)}\ \frac{m-n}{mn}\cdot\frac{2mn}{mn-m^2}=\frac{ (m-n)\cdot2mn}{mn\cdot{m}(n-m)}={-}\frac{ (m-n)\cdot2mn}{mn\cdot{m}(m-n)}={-}\frac{2}{m};\)

\({\largeг)}\ \frac{4ab}{cx+dx}\cdot\frac{ax+bx}{2ab}=\frac{4ab\cdot{x}(a+b)}{ x(c+d)\cdot2ab}=\frac{ 2(a+b)}{c+d}=\frac{2a+2b}{c+d};\)

\({\largeд)}\ \frac{ma-mb}{3n^2}\cdot\frac{2m}{nb-na}=\frac{ m(a-b)\cdot2m}{3n^2\cdot{n}(b-a)}={-}\frac{ m(a-b)\cdot2m}{3n^2\cdot{n}(a-b)}={-}\frac{2m^2}{3n^3};\)

\({\largeе)}\ \frac{ax-ay}{5x^2y^2}\cdot\left({-}\frac{5xy}{by-bx}\right)={-}\frac{ a(x-y)\cdot5xy}{5x^2y^2\cdot{b}(y-x)}=\frac{ a(x-y)\cdot5xy}{5x^2y^2\cdot{b}(x-y)}=\frac{a}{bxy}.\)