Question

计算化简：

6y

x2-y2

-

2

y-x

+

3

x+y

=

5

x-y

．

．

Answer 1

分析：先把各分式的分子或分母因式分解得到原式=

6y

(x+y)(x-y)

+

2

x-y

+

3

x+y

，然后通分得到原式=

6y

(x+y)(x-y)

+

2(x+y)

(x+y)(x-y)

+

3(x-y)

(x+y)(x-y)

，再把分子进行加减运算，得到原式=

6y

(x+y)(x-y)

+

2(x+y)

(x+y)(x-y)

+

3(x-y)

(x+y)(x-y)

，然后约分即可．

解答：解：原式=

6y

(x+y)(x-y)

+

2

x-y

+

3

x+y

=

6y

(x+y)(x-y)

+

2(x+y)

(x+y)(x-y)

+

3(x-y)

(x+y)(x-y)

=

6y+2x+2y+3x-3y

(x+y)(x-y)

=

6y

(x+y)(x-y)

+

2(x+y)

(x+y)(x-y)

+

3(x-y)

(x+y)(x-y)

=

5(x+y)

(x+y)(x-y)

=

5

x-y

．
故答案为

5

x-y

．

点评：本题考查了分式的加减法：先把各分式的分子或分母因式分解，确定各分式的最简公分母，然后把各分式进行通分，再把分子进行加减运算，最后化为最简分式或整式．