Rút gọn các phân thức a, (x^3+y^3+z^3-3yz) / ( x^2+y^2+z^2-xy-yz-zx ) b, (a^8-b^8) / ( a^3-a^2b+ab^2-b^3 )

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)`