004 Sample Final A, Problem 10

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Decompose into separate partial fractions.     

Foundations
1) What is the form of the partial fraction decomposition of ?
2) What is the form of the partial fraction decomposition of ?
Answer:
1)
2)


Solution:

Step 1:
We set .
Step 2:
Multiplying both sides of the equation by , we get
.
Step 3:
If we set in the above equation, we get and .
If we set in the above equation, we get and .
Step 4:
In the equation , we compare the constant terms of both sides. We must have
. Substituting and , we get .
Thus, the partial fraction decomposition is
Final Answer:

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