I know how these problems are rigged to work.

They are quite artifical and what happens is the +1 changes a -.5 to a +.5

Hence MY guess is that the second power is -2 not +2

y= (x^4)/4 + 1/8x^{-2} for 1<x<3

I GUESS you meant to put 1/(8x^2), which I know works.

But your math showed that you wanted (1/8)x^2.