Solution #16

(5x - 11)/(2x²+x-6) = (5x-11)/((2x - 3)(x+2)).

We then write (5x-11)/((2x-3)(x+2)) = A/(2x-3) + B/(x+2).

Multiplying both sides by (2x-3)(x+2), we have:

5x - 11 = A(x+2) + B(2x-3)

5x - 11 = Ax + 2A + 2Bx - 3B

5x - 11 = (A+2B)x + (2A-3B)

Equating coefficients of like terms, we have:

A + 2B = 5
2A - 3B = -11

Doubling the first equation gives 2A + 4B = 10, and subtracting the second from the first gives 7B = 21, and B = 3. Then A = -1, so our sum is:

-1/(2x-3) + 3/(x+2)