若a2=3a-1,则分式2a5-5a4+2a3-8a 2a2+1的值是______.

问题描述:

若a2=3a-1,则分式

2a5-5a4+2a3-8a 2
a2+1
的值是______.

原式=

2a3(a2+1)-a2(5a2+8)
a2+1

=
2a3(3a-1 +1)-a2[5(3a-1)+8]
a2+1

=
2a3•3a-a2[15a+3]
a2+1

=
6(3a-1)2-(3a-1)[15a+3]
a2+1

=
(3a-1)[6(3a-1)-(15a+3)]
a2+1

=
(3a-1)(3a-9)
a2+1

=
9(3a-1)-30a+9
3a

=
-3a
3a

=-1.
故答案为:-1.
答案解析:先根据分式混合运算的法则把原式进行化简,再把a2=3a-1代入进行计算即可.
考试点:分式的化简求值.
知识点:本题考查的是分式的化简求值,熟知分式混合运算的法则是解答此题的关键.