Question

已知M=

x2+y2

x2-y2

，N=

2xy

x2-y2

，用加減號連接M、N的三種不同形式：N+M．M-N，N-M，請你任選兩種形式進行計算．

Answer 1

∵M=

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

．