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：学生作业帮助网编辑：作业帮时间：2024/04/29 21:03:23

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

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

蛟川真变态，让我们做这种题

我也是蛟川的，你几班？最后等于-3

通分。

=[(y-z)^2*-(y-z) + (z-x)^2*-(z-x) + (x-y)^2*-(x-y)]/(x-y)(y-z)(z-x)
=[(z-y)^3 + (x-z)^3 + (y-x)^3)]/(x-y)(y-z)(z-x)
=3[xy(x-y) + yz(y-z) + zx(z-x)]/(x-y)(y-z)(z-x)
=3[xy/(y-z)(z-x) + yz/(x...

全部展开

=[(y-z)^2*-(y-z) + (z-x)^2*-(z-x) + (x-y)^2*-(x-y)]/(x-y)(y-z)(z-x)
=[(z-y)^3 + (x-z)^3 + (y-x)^3)]/(x-y)(y-z)(z-x)
=3[xy(x-y) + yz(y-z) + zx(z-x)]/(x-y)(y-z)(z-x)
=3[xy/(y-z)(z-x) + yz/(x-y)(z-x) + zx/(x-y)(y-z)]

收起

我初一作初三题，太坑爹了

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