This MitPY comes from frequent commenter, John Friend:

*Dear colleagues,*

*I figured this was as good place as any to ask for help. I’m writing a small test on rational functions. One of my questions asks students to consider the function where and to find the values of for which the function intersects its oblique asymptote.*

*The oblique asymptote is so they must first solve*

* … (1)*

*for . The solution is and there are no restrictions along the way to getting this solution that I can see. So obviously .*

*It can also be seen that if then equation (1) becomes which has no solution. So obviously .*

*When I solve equation (1) using Wolfram Alpha the result is also . But here’s where I’m puzzled:*

*Wolfram Alpha gives the obvious restriction but also the restriction .*

* emerges naturally (and uniquely) from this second restriction and I really like that this happens as a natural part of the solution process. BUT ….*

*I cannot see where this second restriction comes from in the process of solving equation (1)! Can anyone see what I cannot? *

*Thanks.*