已知a^2+9b^2+4a-6b+5=0,求代数式[(a+3b)/(a+2b)]/[(a^2+6ab+9b^2)/(a^2-4b^2)]

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已知a^2+9b^2+4a-6b+5=0,求代数式[(a+3b)/(a+2b)]/[(a^2+6ab+9b^2)/(a^2-4b^2)]已知a^2+9b^2+4a-6b+5=0,求代数式[(a+3b)

已知a^2+9b^2+4a-6b+5=0,求代数式[(a+3b)/(a+2b)]/[(a^2+6ab+9b^2)/(a^2-4b^2)]
已知a^2+9b^2+4a-6b+5=0,求代数式[(a+3b)/(a+2b)]/[(a^2+6ab+9b^2)/(a^2-4b^2)]

已知a^2+9b^2+4a-6b+5=0,求代数式[(a+3b)/(a+2b)]/[(a^2+6ab+9b^2)/(a^2-4b^2)]
a^2+9b^2+4a-6b+5=0
a^2+4a+4+9b^2-6b+1=0
(a+2)^2+(3b-1)^2=0
(a+2)^2=0,(3b-1)^2=0
a=-2,b=1/3
[(a+3b)/(a+2b)]/[(a^2+6ab+9b^2)/(a^2-4b^2)]
=[(a+3b)/(a+2b)]/[(a+3b)^2/(a-2b)(a+2b)]
=(a+3b)/(a+2b)*(a-2b)(a+2b)/(a+3b)^2
=(a-2b)/(a+3b)
=(-2-2*1/3)/(-2-1/3*3)
=(-2-2/3)/(-2-1)
=(-8/3)/(-3)
=8/9

a^2+9b^2+4a-6b+5=0,整理得:
(a+2)^2+(3b-1)^2=0
则(a+2)^2=0 (3b-1)^2=0
a=-2 b=1/3
[(a+3b)/(a+2b)]/[(a^2+6ab+9b^2)/(a^2-4b^2)]=[(a+3b)/(a+2b)]/[(a+3b)^2/(a-2b)(a+2b)]
=(a-2b)/(a+3b)
=(-2-2×1/3)/(-2+3×1/3)
=8/3