Решение №126

• а) $$\frac{mx^2-my^2}{2m+8} \cdot \frac{3m+12}{my +mx} = \frac{m(x^2-y^2)\cdot3(m+4)}{2(m+4)\cdotm(y+x)} = \frac{m(x-y)(x+y)\cdot3(m+4)}{2(m+4)\cdotm(x+y)} = \frac{3(x-y)}{2}$$
• б) $$\frac{ax+ay}{x^2-2xy+y^2} \cdot \frac{x^2-xy}{7x+7y} = \frac{a(x+y)x(x-y)}{(x-y)^2 \cdot 7(x+y)} = \frac{ax}{7(x-y)}$$
• в) $$\frac{x^3-y^3}{x+y} \cdot \frac{x^2-y^2}{x^2+xy+y^2} = \frac{(x-y)(x^2+xy+y^2)\cdot(x-y)(x+y)}{(x+y)\cdot(x^2+xy+y^2)} = (x-y)^2 = x^2-2xy + y^2$$
• г) $$\frac{a^2-a+1}{a^3+1} \cdot \frac{a^2+2a+1}{a^2-a+1} = \frac{(a^2-a+1)\cdot(a+1)^2}{(a+1)(a^2-a+1)\cdot(a^2-a+1)} = \frac{a-1}{(a+1)^2}$$