a2+2a+1/a2-1-1/a-1 化简求值 其中a=根号2

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a2+2a+1/a2-1-1/a-1 化简求值 其中a=根号2
a2+2a+1/a2-1-1/a-1 化简求值 其中a=根号2

a2+2a+1/a2-1-1/a-1 化简求值 其中a=根号2
原式=(a+1)²/(a²-1)-1/(a-1)
=((a+1)²-(a+1))/(a²-1)
=(a²+a)/(a²-1)
=a/(a-1)
=√2/(√2-1)
=√2(√2+1)
=2+√2;
如果本题有什么不明白可以追问,

[(a²+2a+1)/(a²-1)]-[1/(a-1)]
=[(a+1)²/(a+1)(a-1)]-[1/(a-1)]
=[(a+1)/(a-1)]-[1/(a-1)]
=a/(a-1)
=√2/(√2-1)
=2+√2