Упражнение 128

\({\largeа)}\ \frac{mx^2-my^2}{2m+8}\cdot\frac{3m+12}{my+mx}=\frac{ m(x^2-y^2)\cdot3(m+4)}{ 2(m+4)\cdot{m}(y+x)}=\frac{ m(x-y)(x+y)\cdot3(m+4)}{ 2(m+4)\cdot{m}(x+y)}=\frac{ 3(x-y)}{2}=\frac{3x-3y}{2};\)

\({\largeб)}\ \frac{ax+ay}{x^2-2xy+y^2}\cdot\frac{x^2-xy}{7x+7y}=\frac{ a(x+y)\cdot{x}(x-y)}{ (x-y)^2\cdot7(x+y)}=\frac{ax}{ 7(x-y)}=\frac{ax}{7x-7y};\)

\({\largeв)}\ \frac{x^3-y^3}{x+y}\cdot\frac{x^2-y^2}{x^2+xy+y^2}=\frac{ (x-y)(x^2+xy+y^2)\cdot(x-y)(x+y)}{ (x+y)\cdot(x^2+xy+y^2)}=(x-y)^2=x^2-2xy+y^2;\)

\({\largeг)}\ \frac{a^2-1}{a^3+1}\cdot\frac{a^2-a+1}{a^2+2a+1}=\frac{ (a-1)(a+1)\cdot(a^2-a+1)}{ (a+1)(a^2-a+1)\cdot(a+1)^2}=\frac{a-1}{ (a+1)^2}=\frac{a-1}{a^2+2a+1}.\)