Question

先化简,再求值[(a+2)/(a^2-2a)+(8)/(4-a^2)]÷(a^2-4)/(a),其中a满足方程a^2+4

Answer 1

a²+4a+1=0

a²+4a=-1

原式=[(a+2)²-8a]/a(a+2)(a-2)×a/(a²-4)

=(a²-4a+4)/a(a+2)(a-2)×a/(a+2)(a-2)

=(a-2)²/a(a+2)(a-2)×a/(a+2)(a-2)

=1/(a+2)²

=1/(a²+4a+4)

=1/(-1+4)

=1/3