SOLUTION: Write the rational expression 7/2x^2-5x-3 as a sum of partial fractions.

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Question 600952: Write the rational expression 7/2x^2-5x-3 as a sum of partial fractions.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Write the rational expression 7/2x^2-5x-3 as a sum of partial fractions.
Factor the denominator and write it
7%2F%28%282x%2B1%29%28x-3%29%29 = A%2F%28%282x%2B1%29%29 + B%2F%28%28x-3%29%29
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Combine the fractions on the right
7%2F%28%282x%2B1%29%28x-3%29%29 = %28A%28x-3%29%2BB%282x%2B1%29%29%2F%28%282x%2B1%29%28x-3%29%29
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If the denominators are equal, the numerators are, we can write it
7 = A(x-3) + B(2x+1)
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Assume this is an identity, equation true for all values of x.
Let x=3
7 = A(3-3) + B(2(3)+1)
The A term drops out
7 = 7B + 0
B = 1
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Let x=-.5
7 = A(-.5-3) + B(2(-.5)+1)
The B term drops out
7 = -3.5A + 0
A = -2
:
The decomposed fraction
7%2F%28%282x%2B1%29%28x-3%29%29 = %28-2%29%2F%28%282x%2B1%29%29 + 1%2F%28%28x-3%29%29