SOLUTION: 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?
Algebra ->
Matrices-and-determiminant
-> SOLUTION: 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?
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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):
You can verify the answer by graphing each side of the equation
as two separate equations
In other words, set the left side equal to y to get and graph that. Then graph (the right side)
You'll then find that the two graphs match up (ie one graph is right on top of the other), which confirms that they are equal. You can even compare the table of values for each equation and you'll find that the two tables are identical.
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