This MitPY comes from frequent commenter, John Friend:
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
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?