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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