Write out the form of the partial fraction decomposition of the function. do not determine the numerical values of the coefficients. (if the partial fraction decomposition does not exist, enter dne.)

For part (a), you have




If , then .

If , then .

So,



For part (b), since the degrees of the numerator and denominator are the same, you first need to find the quotient and remainder upon division.



In the remainder term, the denominator can't be factorized into linear components with real coefficients, since the discriminant is negative . However, you can still factorized over the complex numbers, so a partial fraction decomposition in terms of complexes does exist.





Then you have




When , you have





When , you have





So, you could write



but that may or may not be considered acceptable by that webpage.