若x+1/x=3,则x方/(x四次+x方+1)的值为

问题描述:

若x+1/x=3,则x方/(x四次+x方+1)的值为

x+1/x=3
(x+1/x)²=3²
x²+1/x²+2*x*1/x=9
x²+1/x²+2=9
x²+1/x²=7
x方/(x四次+x方+1)
=1/(x四次/x²+x方/x²+1/x²)
=1/(x²+1+1/x²)
=1/(7+1)
=1/8