Numerical solution: We could substitute numbers which increase in size: `100`, then `10\ 000`, then `1\ 000\ 000`, etc and we would find that the value approaches `-1/8`.

Algebraic solution:

We first divide top and bottom of our fraction by `x^2`, then take limits.

`lim_(x->oo)((1-x^2)/(8x^2+5))`

`=lim_(x->oo)((1/x^2-x^2/x^2)/((8x^2)/(x^2)+5/x^2))`

`=lim_(x->oo)((1/x^2-1)/(8+5/x^2))`

`=-1/8`