来自邵立平的问题
化简:x2+yzx2+(y−z)x−yz+y2−zxy2+(z+x)y+zx+z2+xyz2−(x−y)z−xy=______.
化简:x2+yzx2+(y−z)x−yz+y2−zxy2+(z+x)y+zx+z2+xyz2−(x−y)z−xy=______.
1回答
2020-05-0112:25
化简:x2+yzx2+(y−z)x−yz+y2−zxy2+(z+x)y+zx+z2+xyz2−(x−y)z−xy=______.
化简:x2+yzx2+(y−z)x−yz+y2−zxy2+(z+x)y+zx+z2+xyz2−(x−y)z−xy=______.
∵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,
∴x