Given the equation $e^x=\frac{bx-a}{c+dx}$ where : $a,b,c,d \in R$ and $a+c=-1$, how can I prove that there are at most two real solutions? Graphically it's pretty clear to see since there is an exponential and a hyperbole, but formally how one should prove this? Many thanks.
EDIT : I am looking for positive solutions only.
EDIT : Prove a convex and concave function can have at most 2 solutions here I’ve found the answer to my question.