I understand the first problem to be:Originally Posted by roseh
So. You want to decompose the fraction into linear (or nonfactorable quadratic) parts.
Where A and B are some constants.
There are various and sundry ways to solve for A and B. My favorite is simply to add the two fractions and compare the numerator with the numerator of the original expression. So:
So we know that .
By expanding the LHS and matching like coefficients we get that A+B=0 and -A=1. So A=-1 and B=1. Finally: