17. Simplify first and then evaluate: [2a/(a-1)+a/(1-a)] ÷ a, where a=√2+ 1.
Solution: [2a/(a-1)+a/(1-a)] \ a.
=[2a/(a- 1)-a/(a- 1)]\a
=[(2a-a)/(a- 1)]\a
=a/(a- 1)÷a
= 1/(a- 1)
Substitute a=√2+ 1 into the above formula, and you get
= 1/(√2+ 1- 1)
= 1/√2
=√2/2?
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