Concept explainers
To find: The partial fraction decomposition of the given rational function.
Answer to Problem 38AYU
Solution:
Explanation of Solution
Given:
Formula used:
a. If then partial fraction decomposition of takes the form:
where are to be determined.
b. If has repeated linear factor of the form an integer, then, in the partial fraction decomposition of , takes the form:
where the numbers are to be determined.
Calculation:
The denominator of the rational function can be factored as
The denominator has repeated linear factor x and non repeated linear factor . Therefore the partial raction decomposition takes the form
-----Eq (1)
Equating the co-efficients on both sides in Eq(1),
-----Eq(2)
-----Eq(3)
-----Eq(4)
-----Eq(5)
-----Eq(6)
Solving for from Eq(2) – Eq(6) we get
The partial fraction decomposition of is
Chapter 11 Solutions
Precalculus
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