ln(A)=ln(B)-ln(1-B); solve for B
ln(A)=ln(B/(1-B)) condense right side
e^(lnA)=e^(ln(B/(1-B)) exponentiate with base e on both sides and inverse property gives:
A=B/(1-B)
(1-B)A=B multiplication property of equality
A-AB=B distributive property
A=B+AB addition property of equality
A=B(1+A) distributive property
A/(1+A)=B division property of equality