Common Denominators, What is A + B

Question

I've found the common denominators and then played around with the stuff in the numerator, but the question asks specifically $A + B$. Is that even possible to find since we have A - B on the left hand side?

So I got $A(x+2) - B(x-3) = 3x + 16$

Just not sure if you can solve for an $A + B$. Thanks for any help.

Answer 1

Hint: You write,

I got $$ A(x+2) - B(x-3) = 3x + 16. $$

The left hand side can be simplified into the form $$ \text{something}~x + \text{somethingElseWithoutX} $$

I'll get you started: $A(x + 2) = Ax + 2A$.

Try doing that, and see what you learn about $A$ and $B$.