化简(y-x)(z-x)/(x-2y+z)(x+y-2z)+(z-y)(x-y)/(x-2z+y)(y+z-2x)+(x
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化简(y-x)(z-x)/(x-2y+z)(x+y-2z)+(z-y)(x-y)/(x-2z+y)(y+z-2x)+(x-z)(y-z)/(y+z-2x)(x-2y+z)
∵x-2y+z=(x-y)-(y-z),x+y-2z=(y-z)-(z-x),y+z-2x=(z-x)-(x-y).
设x-y=a,y-z=b,z-x=c,则
原式=-ac/ (a-b)(b-c) +(-ba)/(b-c)(c-a) +(-cb)/(c-a)(a-b)
=-ac(c-a)+ba(a-b)+bc(b-c)/(a-b)(b-c)(c-a)
=-ac²-a²c+ba²-b²a+b²c-bc² /(a-b)(b-c)(c-a)
=-c²(a-b)-c(a²-b²)+ab(a-b) /(a-b)(b-c)(c-a)
=-(a-b)(c²-ca-cd+ab)/(a-b)(b-c)(c-a)
=-(a-b)(c-a)(c-b)/(a-b)(b-c)(c-a)
=1.
设x-y=a,y-z=b,z-x=c,则
原式=-ac/ (a-b)(b-c) +(-ba)/(b-c)(c-a) +(-cb)/(c-a)(a-b)
=-ac(c-a)+ba(a-b)+bc(b-c)/(a-b)(b-c)(c-a)
=-ac²-a²c+ba²-b²a+b²c-bc² /(a-b)(b-c)(c-a)
=-c²(a-b)-c(a²-b²)+ab(a-b) /(a-b)(b-c)(c-a)
=-(a-b)(c²-ca-cd+ab)/(a-b)(b-c)(c-a)
=-(a-b)(c-a)(c-b)/(a-b)(b-c)(c-a)
=1.
化简(y-x)(z-x)/(x-2y+z)(x+y-2z)+(z-y)(x-y)/(x-2z+y)(y+z-2x)+(x
(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)/(xy-2z)(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)
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=?
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
x,y,z为实数且(y-z)平方+(x-y)平方+(z-x)平方=(y+z-2x)平方+(z+x-2y)平方+(x+y-