Calculus 2 writing partial fraction decomposition (7.4 1)

Question

Write out the general form of the partial fraction decomposition of the function. Do not determine the numerical values of the constants.

1) x-20/x²-x-20

2) x²/x²+20+20

Please show all steps for each problem, box the final answer, thank you.

Answer 1

1) x-20 a b

------------- = -------- + -------------

x^2-x-20 (x-5) x+4

2) are you sure the denominator isn't meant to be x^2+20x+20 ?????

Either way, long division is required... I will use the problem as posted which is x^2/(x^2+40)

1

_____________

As written, x^2 + 40 | x^2

x^2 + 40

---------------------

-40

applies linearity property to (1- 40/(x^2+40))

integral [1] - 40 integral[ 1/(x^2+40) ]

1 integrates to x

the p.f.d of the second integral is (ax+b)/(x^2+40)

the unfactorable, irreducable quadratic takes a linear function in the numerator