(3x+y)/(x^2+xy) - (x+3y)/(y^2+xy) упростите выражение

Question

(3x+y)/(x^2+xy) - (x+3y)/(y^2+xy) упростите выражение

Answer 1

(3x+y)/(x²+xy)-(x+3y)/(y²+xy)=((3x+y)(y²+xy)-(x+3y)(x²+xy))/((x²+xy)(y²+xy))=
=3xy²+3x²y+y³+xy²+y³-xy²-3x²y-x³-3xy²)/(x²y²+xy³+x³y+x²y²)=
=(y³-x³)/(xy³+2x²y²+x³y)=(y³-x³)/((xy*(y²+2xy+x²))=(y³-x³)/((xy*(y+x)²).