Question

(

x2+y2

xy

-

x2

xy+y2

-

y2

x2+xy

)÷

3

xy

．

Answer 1

分析：原式括號(hào)中通分并利用同分母分式的減法法則計(jì)算，同時(shí)利用除以一個(gè)數(shù)等于乘以這個(gè)數(shù)的倒數(shù)將除法運(yùn)算化為乘法運(yùn)算，約分即可得到結(jié)果．

解答：解：原式=[

(x2+y2)(x+y)

xy(x+y)

-

x3

xy(x+y)

-

y3

xy(x+y)

]•

xy

3

=

x2+y2

3(x+y)

-

x3

x+y

-

y3

3(x+y)

=

x2+y2-3x3-y3

3(x+y)

．

點(diǎn)評(píng)：此題考查了分式的混合運(yùn)算，分式的加減運(yùn)算關(guān)鍵是通分，通分的關(guān)鍵是找最簡(jiǎn)公分母；分式的乘除運(yùn)算關(guān)鍵是約分，約分的關(guān)鍵是找公因式．