分析:把各分母分別分解因式,然后通分并進(jìn)行計(jì)算,求出分子等于0,結(jié)果即可得到.
解答:解:∵x
2+(y-z)x-yz=x
2+xy-xz-yz=x(x+y)-z(x+y)=(x+y)(x-z),
y
2+(z+x)y+zx=y
2+zy+zy+zx=y(y+z)+z(x+y)=(x+y)(y+z),
z
2-(x-y)z-xy=z
2-xz+yz-xy=z(z-x)+y(z-x)=(y+z)(z-x),
∴通分公分母是(x+y)(y+z)(z-x),
分子是:-(x
2+yz)(y+z)+(y
2-zx)(z-x)+(z
2+xy)(x+y),
=(-x
2y-x
2z-y
2z-z
2y)+(y
2z-y
2x-z
2x+x
2z)+(z
2x+z
2y+x
2y+y
2x),
=(-x
2y+x
2y)+(-x
2z+x
2z)+(-y
2z+y
2z)+(-z
2y+z
2y)+(-y
2x+y
2x)+(-z
2x+z
2x),i
=0,
∴
++=
=0.
故答案為:0.
點(diǎn)評(píng):本題考查了對(duì)稱(chēng)式與輪換式的運(yùn)算,對(duì)分母分解因式找出公分母,然后通分,對(duì)分子進(jìn)行準(zhǔn)確計(jì)算是解題的關(guān)鍵,運(yùn)算量較大,計(jì)算時(shí)要認(rèn)真細(xì)心.