化简 [x^3(y^2-z^2)+y^3(z^2-x^2)+z^3(x^2-y^2)]/[x^3(y-z)+y^2(z-x)+z^3(x-y)]=

题目

化简 [x^3(y^2-z^2)+y^3(z^2-x^2)+z^3(x^2-y^2)]/[x^3(y-z)+y^2(z-x)+z^3(x-y)]=
是y^3.
正确的是化简 [x^3(y^2-z^2)+y^3(z^2-x^2)+z^3(x^2-y^2)]/[x^3(y-z)+y^3(z-x)+z^3(x-y)]=

答案

貌似分母的倒数第二项应该是y^3吧.
分子拆括号再提取公因式得(xy)^2(x-y)+(xz)^2(z-x)+(yz)^2(y-z)
分母拆括号再提取公因式得(xy)(x+y)(x-y)+(xz)(z+x)(z-x)+(yz)(y+z)(y-z)