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Question 381369: Write the partial fraction decomposition of the following rational expression.
(x^2-x-8)/(x+1)(x^2+5x+6)
For this type of problem, how can I check if my answer is correct?
Here is how I solved the problem:
First, I factored the denominator.
(x^2-x-8)/(x+1)(x+3)(x+2)
Then, (A)/(x+1) + (B)/(x+3) + (C)/(x+2)
Multiplied all by LCD to get rid of fractions, left with: (x^2-x-8)=A(x+3)(x+2)+B(x+1)(x+2)+C(x+3)(x+1)
Solved for A first by letting x=-1, that way B and C drop out.
A=-3
Solved for B by letting x=-3 so A and C drop out.
B=2
Solved for C by letting x=-2 so A and B drop out.
C=2
I plug in A, B, and C back into this (A)/(x+1) + (B)/(x+3) + (C)/(x+2) and my final answer is:
((-3)/(x+1))+((2)/(x+3))+((2)/(x+2))
Is this correct? Also, how can I verify in the future if my answer is correct if for example I have to do a similar problem on an exam?
Answer by jim_thompson5910(35256)   (Show Source):
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