Question

已知：x+

2

x

=3； x+

6

x

=5； x+

12

x

=7，根據(jù)以上規(guī)律，求x+

n2+n

x-3

=2n+4的解．

Answer 1

考點(diǎn)：分式方程的解

專題：

分析：根據(jù)計(jì)算、觀察，可得規(guī)律：x+

n2+n

x

=2n+1，的解為=n或x=n+1，根據(jù)規(guī)律，可得答案．

解答：解：x+

2

x

=3可轉(zhuǎn)化為x²-3x+2=0，解得x₁=1，x₂=2，
 x+

6

x

=5可轉(zhuǎn)化為x²-5x+6=0解得x₁=2，x₂=3，
x+

n2+n

x

=2n+1，的解為=n或x=n+1，
x+

n2+n

x-3

=2n+4可轉(zhuǎn)化為x-3+

n2+n

x-3

=2n+1，得x-3=n或x-3=n+1，
x₁=n+3，x₂=n+4．

點(diǎn)評(píng)：本題考查了分式方程的解，發(fā)現(xiàn)規(guī)律是解題關(guān)鍵．