Common-intercept partial fraction identity
= Common-intercept partial fraction identity
{title2=$\frac1{(A+mx)(A+nx)}=\frac1{A(m-n)}\left(\frac m{A+mx}-\frac n{A+nx}\right)$}
For $A\ne0$ and $m\ne n$, combining the right-hand fractions gives numerator $A(m-n)$ and proves the identity. Integration on an interval avoiding the poles gives $\ln|(A+mx)/(A+nx)|/[A(m-n)]$ plus a constant. The overall $1/A$ cannot be dropped unless the variable has already been normalized to $A=1$.