The form of the partial fraction decomposition of a rational function is given below. 5x^2+3x+54/(x+3)(x^2+9)=a/x+3+bx+c/ x^2+9 find a, b,and c

Step-by-step explanation:

The partial fraction decomposition is given as:

We collect LCD on the RHS to obtain;

We expand the parenthesis in the numerator of the fraction on the RHS.

This implies that:

This is now an identity. Since the denominators are equal, the numerators must also be equal.

We compare coefficients of the quadratic terms to get:

Also the coefficients of the linear terms will give us:

The constant terms also gives us;

Put equation (1) in to equations (2) and (3).

Put equation (4) into (5).

Do backward substitution to get:

answer: (-6,3)

step-by-step explanation: