化簡(jiǎn):
x2+yz
x2+(y-z)x-yz
+
y2-zx
y2+(z+x)y+zx
+
z2+xy
z2-(x-y)z-xy
=
 
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:∵x2+(y-z)x-yz=x2+xy-xz-yz=x(x+y)-z(x+y)=(x+y)(x-z),
y2+(z+x)y+zx=y2+zy+zy+zx=y(y+z)+z(x+y)=(x+y)(y+z),
z2-(x-y)z-xy=z2-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:-(x2+yz)(y+z)+(y2-zx)(z-x)+(z2+xy)(x+y),
=(-x2y-x2z-y2z-z2y)+(y2z-y2x-z2x+x2z)+(z2x+z2y+x2y+y2x),
=(-x2y+x2y)+(-x2z+x2z)+(-y2z+y2z)+(-z2y+z2y)+(-y2x+y2x)+(-z2x+z2x),i
=0,
x2+yz
x2+(y-z)x-yz
+
y2-zx
y2+(z+x)y+zx
+
z2+xy
z2-(x-y)z-xy
=
0
(x+y)(y+z)(z-x)
=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.
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