Question

計算化簡：

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)

，再把分子進行加減運算，得到原式=

6y

(x+y)(x-y)

+

2(x+y)

(x+y)(x-y)

+

3(x-y)

(x+y)(x-y)

，然后約分即可．

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

．
故答案為

5

x-y

．

點評：本題考查了分式的加減法：先把各分式的分子或分母因式分解，確定各分式的最簡公分母，然后把各分式進行通分，再把分子進行加減運算，最后化為最簡分式或整式．