I have this equation:
2/((x+3)(x+5))
and I want to rewrite it in this way:
A/(x+3) + B/(x+5)
How many ways do I have to rewrite it? I personally think that the only solution is that A = 1 and B = -1. But an acquaintance of mine says there are infinitely many. Could someone help me win my case

Thank you!
: )

This is the procedure I used to find the solution for A and B.
2/((x+3)(x+5)) = A/(x+3) + B/(x+5)
then by calculating the lowest common denominator and simplifying a bit I arrived here:
2 = A*(5x) + B(3*x)
And lastly if we substitute x first for -3 and then for -5, we find our solutions.
I cannot find any other solutions.