There are real numbers A and B such that (5x + 16)/(x^2 - 7x + 10) = A/(x - 2) + B/(x - 5). Find A + B.
Note that x^2 -7x + 10 = (x - 2) ( x - 5)
Multiply through by the factorized form and we have
5x + 16 = A ( x - 5) + B ( x - 2)
5x + 16 = (A + B)x + ( -5A - 2B)
Equating terms we see that
A + B = 5
