计算下列各式：（1）1a−b+1a+b+2aa2+b2+4a3a4+b4；（2）x2+yzx2+(y−z)x−yz+y2−zxy2+(z+x)y+zx+z2+xyz2−(x−y)z−xy；（3）x3−1x3+2x2+2x+1+x3+1x3−2x2+2x−1−2(x2+1)x2−1（4）(y−x)(z−x)(x−2y+z)(x+y−2z)+(z−y)(x−y)

Question

计算下列各式：
（1）(1)/(a−b)+(1)/(a+b)+(2a)/(a2+b2)+(4a3)/(a4+b4)；
（2）(x2+yz)/(x2+(y−z)x−yz)+(y2−zx)/(y2+(z+x)y+zx)+(z2+xy)/(z2−(x−y)z−xy)；
（3）(x3−1)/(x3+2x2+2x+1)+(x3+1)/(x3−2x2+2x−1)−(2(x2+1))/(x2−1)
（4）((y−x)(z−x))/((x−2y+z)(x+y−2z))+((z−y)(x−y))/((x+y−2z)(y+z−2x))+((x−z)(y−z))/((y+z−2x)(x−2y+z))．

Answer 1

（1）(1)/(a−b)+(1)/(a+b)+(2a)/(a2+b2)+(4a3)/(a4+b4)
=(2a)/(a2−b2)+(2a)/(a2+b2)+(4a3)/(a4+b4)
=(4a3)/(a4−b4)+(4a3)/(a4+b4)
=(8a7)/(a8−b8)；
（2）(x2+yz)/(x2+(y−z)x−yz)+(y2−zx)/(y2+(z+x)y+zx)+(z2+xy)/(z2−(x−y)z−xy)
=(x(x−z)+z(x+y))/((x+y)(x−z))+(y(x+y)−x(y+z))/((x+y)(y+z))+(z(y+z)−y(z−x))/((z−x)(y+z))
=(x)/(x+y)+(z)/(x−z)+(y)/(y+z)-(x)/(x+y)-

作业帮用户 2017-10-02 举报