若a^2+3a+1=0,求代数式a^4+3a^3-a^2-5a+1/a-2的值

a^4+3a^3-a^2-5a+1 = a^2（a^2+3a+1）-2（a^2+3a+1）+a+3 剩下的自己算吧 后面你写的没看太明白 那个a-2是分母呢还是什么

a^2+3a=-1

a^4+3a^3-a^2-5a+1/a-2
=a^2(a^2+3a)-(a^2+3a)-2a+1/a-2
=-a^2+1-2a+1/a-2
=-(a^2+3a)+a+1/a-1
=1+(a^2+a)/a-1
=(a^2+a)/a
=(a^2+3a)/a-2
=-1/a-2

(a^4+3a^3-a^2-5a+1)/(a-2)
=[(a^4+3a^3+a^2)+(-2a^2-6a-2)+a+3]
=[a^2(a^2+3a+1)-2(a^2+3a+1)+a+3]
=[(a^2+3a+1)(a^2-2)+a+3]/(a-2)
=(a+3)/(a-2)