Partial fraction division

[gritty nymph]

I need some help with this.

Translation:
"Partial fraction division of rational functions is useful in several contexts; for example integration of rational functions and inverse Laplace transform. Determine the coefficients a, b, c and d."

Thanks in advance!

[cerulean void]

Multiply both sides by the denominator of the left side.
You will get polynomials on both sides. Since they must be equal, their coefficients at the respective powers of x must all be equal. So, you will have a system of linear equations in a, b, c, d.

[gritty nymph]

I got a = 1, b = 4, c = 3 and d = -5.