There are real numbers A and B such that
(5x + 16)/(x^2 - 7x + 10) = A/(x - 2) + B/(x - 5).
Find A + B.
We can start off by multiplying \(x^2-7x+10\) on both sides which cancels out the denominators.
\(5x+16 = A \cdot (x-5) + B \cdot (x-2) \\ 5x+16 = Ax-5A + Bx-2B \\ 5x+16 = (A+B)x - 5A - 2B\)
Because -5A-2B will not result in something in terms of x, we can ignore it and 16. So we are left with,
\(5x = (A+B)x \\ A+B = 5\)
So A+B = 5.