问题 解答题
化简
2x-y-z
x2-xy-xz+yz
+
2y-x-z
y2-xy-yz+xz
+
2z-x-y
z2-xz-yz+xy
答案

原式=

(x-y)+(x-z)
(x-y)(x-z)
+
(y-x)+(y-z)
(y-x)(y-z)
+
(z-x)+(z-y)
(z-x)(z-y)

=

1
x-z
+
1
x-y
+
1
y-z
+
1
y-x
+
1
z-y
+
1
z-x

=

1
x-z
-
1
x-z
+
1
x-y
-
1
x-y
+
1
y-z
-
1
y-z

=0+0+0

=0.

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