当X=2008时,求代数式(x²-1)(x²+1)/x²-x 除以 [1+(x²+1)/2x]的值

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当X=2008时,求代数式(x²-1)(x²+1)/x²-x 除以 [1+(x²+1)/2x]的值
当X=2008时,求代数式(x²-1)(x²+1)/x²-x 除以 [1+(x²+1)/2x]的值

当X=2008时,求代数式(x²-1)(x²+1)/x²-x 除以 [1+(x²+1)/2x]的值
1+(x²+1)/2x
=(x²+2x+1)/2x
=(x+1)²/2x
(x²-1)(x²+1)/x²-x 除以 [1+(x²+1)/2x]
=(x-1)(x+1)(x²+1)/x(x-1) *2x/(x+1)²
=2(x²+1)/(x+1)
=[2(x²+2x+1)-4x]/(x+1)
=2(x+1)-4x/(x+1)
=2(x+1)-(4x+4-4)/(x+1)
=2(x+1)-4+4/(x+1)
=2(x-1)+4/(x+1)
=2*2007+4/2009
=4014+4/2009

原始化简得:2(x²+1)/x+1
将x=2008=2000+8 代入计算即可得出结果