Question

化简

2x-y-z

x2-xy-xz+yz

+

2y-x-z

y2-xy-yz+xz

+

2z-x-y

z2-xz-yz+xy

．

Answer 1

分析：先把分母分解得出

(x-y)+(x-z)

(x-y)(x-z)

+

(y-x)+(y-z)

(y-x)(y-z)

+

(z-x)+(z-y)

(z-x)(z-y)

，根据分式的除法得出

1

x-z

+

1

x-y

+

1

y-z

+

1

y-x

+

1

z-y

+

1

z-x

，把互为相反数的数相加即可．

解答：解：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．

点评：本题考查了分式的加减混合运算，题目比较典型，并且有一定的难度．