已知x/x²+x+1=a,试求分式x²/x四次方+x²+1

题目

已知x/x²+x+1=a,试求分式x²/x四次方+x²+1

答案

x/(x²+x+1)=a
(x²+x+1)/x=1/a=x+1/x+1
x+1/x=1/a-1
x²/x四次方+x²+1
=1/(x^2+1/x^2+1)
=1/[(x+1/x)^2-1]
=1/[(1/a-1)^2-1]
=a^2/(1-2a)