a math

Let f(x) = 1 / (x2 + 5x + 6)

f(x) = 1 / (x + 2)(x + 3)

Now, let f(x) = A / (x + 2) + B / (x + 3) [Partial fraction]

1 / (x + 2)(x + 3) = [(A + B)x + (3A + 2B)] / (x + 2)(x + 3)

Comparing coefficients:

A + B = 0

3A + 2B = 1

Solving, B = -1, A = 1

So, f(x) = 1 / (x2 + 5x + 6) = 1 / (x + 2) - 1 / (x + 3)