a) `ĐK: x\ne y\ne z`
Dễ dàng CM được: `x^3+y^3+z^3=(x+y+z)(x^2+y^2+z^2-xy-yz-zx)`
`⇒(x^2+y^3+z^3)/(x^2+y^2+z^2-xy-yz-zx)=[(x+y+z)(x^2+y^2+z^2-xy-yz-zx)]/(x^2+y^2+z^2-xy-yz-zx)=x+y+z`
b) `ĐK: a\ne b; a,b>0`
`(a^8-b^8)/(a^3-a^2b+ab^2-b^3)`
`=[(a^4-b^4)(a^4+b^4)]/[(a^3-a^2b)+(ab^2-b^3)]`
`=[(a^2+b^2)(a^2-b^2)(a^4+b^4)]/[a^2(a-b)+b^2(a-b)]`
`=[(a^2+b^2)(a-b)(a+b)(a^4+b^4)]/[(a^2+b^2)(a-b)]`
`=(a+b)(a^4+b^4)`