We find the values of A and B by multiplying both sides by (2x + 1)(x + 4):

3x = A(x + 4) + B(2x + 1)

Then we expand and collect like terms:

3x = (A + 2B)x + (4A + B)

Next, we equate the x terms and the constant terms:

3 = A + 2B 0 = 4A + B

Solving this set of simultaneous equations gives:

A = -B/4

7B/4 = 3

B = 12/7

A = -3/7

So