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

来源：学生作业帮编辑：大师作文网作业帮分类：数学作业时间：2024/11/15 19:23:19

令x-y=a,y-z=b,z-x=c,原式化为-b^2/ac-c^2/ab-a^2/bc,通分得-(a^3+b^3+c^3)/abc,
而a^3+b^3=(a+b)(a^2-ab+b^2),注意到a+b=-c,故原式继续化为-(a^2-ab+b^2+c^2)/ab
而c^2=(a+b)^2
继续化为-（2a^2+ab+2b^2)/ab,拆开即-2a/b-1-2b/a,此时将abc代入通分
再问：求答案啊最后答案！！

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=? 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