Find the solution of a complex equation

Question

Find the solution $x$ of the equation $$ \frac{{Ae^{\frac{{Cx}} {{{\left( {1 - x}\right)}^{D} }}} }}{{1 + Bx}} = x $$ where $A$,$B$,$C$ and $D$ are the constant coefficients. If the solution of above equation can't be obtained, I want to ask to find the solution x of the equation $$ \frac{{Ae^{Cx} }}{{1 + Bx}} = x $$ where $A$,$B$,$C$ are the constant coefficients.