Question

（1997•武漢）計(jì)算（x+y）•

x2

x2-y2

+

y2

x-y

-

2x2y-2xy2

x2-2xy+y2

，正確的結(jié)果為（　�。�

• A．x+y
• B．x-y
• C．y-x
• D．

  x-y

  x+y

Answer 1

分析：先分解因式約分，根據(jù)同分母分式相加減進(jìn)行計(jì)算，最后化成最簡(jiǎn)即可．

解答：解：原式=（x+y）•

x2

(x+y)(x-y)

+

y2

x-y

-

2xy(x-y)

(x-y)2

=

x2

x-y

+

y2

x-y

-

2xy

x-y

=

x2+y2-2xy

x-y

=x-y．
故選B．

點(diǎn)評(píng)：本題考查了分式的混合運(yùn)算的應(yīng)用，注意：先算乘法，再算加減，最后化成最簡(jiǎn)即可．