Question

помогите с этим заданием

Answer 1

1) x-4xy/(x+y)+y=x+y-4xy/(x+y)=(x^2+2xy+y^2-4xy)/(x+y)=(x^2-2xy+y^2)/(x+y)=(x-y)^2/(x+y)

2) x/(y+x)-y/(y-x)-2xy/(x^2-y^2)=x/(x+y)+y/(x-y)-2xy/((x-y)(x+y))=(x^2-xy+xy+y^2-2xy)/((x-y)(x+y))=(x^2-2xy+y^2)/((x-y)(x+y))=(x-y)^2/((x-y)(x+y))=(x-y)/(x+y)

3) (x-y)^2/(x+y) : (x-y)/(x+y)=x-y, что и требовалось доказать
Ответ: доказано