How do I write the partial fraction decomposition of 7/(x^2+13x+40)?

Answer 1

the fractions will be

A/(x+8) + B/(x+5)

A(x+5) + B(x+8) = 7
(A+B)x + (5A+8B) = 0x + 7

A+B = 0
5A+8B = 7
3B = 7
B = 7/3
A = -7/3

7/(x^2+13x+40) = (7/3)/(x+5) - (7/3)/(x+8))