Partial fraction decomposition - Precal?

Question

(3x+2)/(x^4-4x^2)

Answer 1

Factor the denominator of above fraction.

           

           

Equate the coefficients

Equate the   coefficients

Equate the x  coefficients

Equate the  constants

.

Answer 2

Continuous ...

Now solve the above 4 equations.

From equation (4)

From equation (3)

Substitute the value of A in equation (1).

Substitute the value of B in equation (2).

Multiple each side of equation C + D = 3/4 by 2.

To eliminate the D variable add equations (6) and (7).

Substitute the values of A, B in equation (1).

Substitute the values of A, B , C, D in equation (i).

 

Partial decomposition is