This time it is not so obvious what the limit value is. We could substitute larger and larger values of x until we could see what was happening (try `100`, then `1\ 000`, then `1\ 000\ 000` and so on).

Or, we could rearrange the expression and use the fact that


to find the limiting value.

We divide throughout by x to get the expression in a form where we can evaluate it.





Notice that we cannot substitute ∞ into the fraction `((5/x-3)/(6+1))`, because this does not make mathematical sense.

Please do not write `((5-3(oo))/(6(oo)+1))`. It really upsets mathematicians.