(y-x)/(x+z-2y)(x+y-2z)+(z-y)(x-y)/(x+y-2z)(y+z-2x)+(x-z)(y-z

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/10 06:40:40

(y-x)/(x+z-2y)(x+y-2z)+(z-y)(x-y)/(x+y-2z)(y+z-2x)+(x-z)(y-z)/(y+z-2x)(x+z-2y)的值
我已经做到这了：设(X-Y)为a （Z-Y)为b (Z-X)为c
则原题= (-a*-c)/-(a+b)(b+c)+ab/-(c+b)(a+c)+c*-b/(-a+c)(a+b)

∑是循环和
例如
∑a=a+b+c
∑a^2=a^2+b^2+c^2
∑(z-y)(x-y)/(x+y-2z)(y+z-2x)
＝∑(z-y)(x-y)(x+z-2y)/(x+y-2z)(y+z-2x)(x+z-2y)
＝[1/(x+y-2z)(y+z-2x)(x+z-2y)]∑(z-y)(x-y)(x+z-2y)
你的设法不科学,丧失了轮转对称性!
x-y=a
y-z=b
z-x=c
a+b+c=0
∑(z-y)(x-y)(x+z-2y)
=∑(z-y)(x-y)(x-y)+∑(z-y)(x-y)(z-y)
=-∑aab+∑bba
=(a-b)(b-c)(c-a)
1/(x+y-2z)(y+z-2x)(x+z-2y)
=1/(b-c)(c-a)(a-b)
所求＝1

(y-x)/(x+z-2y)(x+y-2z)+(z-y)(x-y)/(x+y-2z)(y+z-2x)+(x-z)(y-z x,y,z正整数 x>y>z证明 x^2x +y^2y+z^2z>x^(y+z)*y^(x+z)*z^(x+y) 化简(y-x)(z-x)/(x-2y+z)(x+y-2z)+（z-y)(x-y)/(x-2z+y)(y+z-2x)+(x (x-2y+z)(x+y-2z)分之（y-x)(z-x) + (x+y-2z)(y+z-2x)分之(z-y)(x-y) 化简(y-x)(z-x)/(x-2y+z)(x+y-2z)+（z-y)(x-y)/(xy-2z)(y+z-2x)+(x- 试证明(x+y-2z)+(y+z-2x)+(z+x-2y)=3(x+y-2z)(y+z-2x)(z+x-2y) (x+y-z)(x-y+z)= (x+y+z)^2-(x-y-z)^2 分式约分:(y+z-x)/{x^2-(y+z)^2} (x+y-z)^2-(x-y+z)^2=? 设x、y、z为整数,证明:x^4*(y-z)+y^4*(z-x)+z^4*(x-y)/(y+z)^2+(z+x)^2+( x,y,z为实数且(y-z)^2+(x-y)^2+(z-x)^2=(y+z-2x)^2+(x+z-2y)^2+(x+y