Question

已知M=

x2+y2

x2-y2

，N=

2xy

x2-y2

，用加減號(hào)連接M、N的三種不同形式：N+M．M-N，N-M，請(qǐng)你任選兩種形式進(jìn)行計(jì)算．

Answer 1

分析：將M與N代入N+M，N-M中計(jì)算即可得到結(jié)果．

解答：解：∵M(jìn)=

x2+y2

x2-y2

，N=

2xy

x2-y2

，
∴N+M=

x2+y2+2xy

x2-y2

=

(x+y)2

(x+y)(x-y)

=

x+y

x-y

；N-M=

x2+y2-2xy

x2-y2

=

(x-y)2

(x+y)(x-y)

=

x-y

x+y

．

點(diǎn)評(píng)：此題考查了分式的加減法，熟練掌握運(yùn)算法則是解本題的關(guān)鍵．