We set:

`(3x)/((2x+1)(x+4))` `A/(2x+1)+B/(x+4)`

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 `x` and constant terms:

The `x` terms: gives `3 = A + 2B`

The constant terms gives: `0 = 4A + B`

Solving this set of simultaneous equations gives:

`A = -B/4`

`7B/4 = 3`

`B = 12/7`

`A = -3/7`

So `(3x)/((2x+1)(x+4))` `=(-3)/(7(2x+1))+12/(7(x+4))`