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Question 209055: use partial functions to decompose the expression 17n-23 / 4n^2+23n-6
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! use partial functions to decompose the expression 17n-23 / 4n^2+23n-6
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Factor the denominator to get (n+6)(4n-1)
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Set up the partial fractions:
A/(n+6) + B/(4n-1)
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Simplify:
[A(4n-1) + B(n+6)]/(4n^2+23n-6)
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[4An + Bn -A + 6B]/ denominator
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= [ (4A+B)n + (-A+6B)]/denom
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Equate to the original fraction to see that
4A+B = 17
-A+6B = -23
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Solve this system to get:
A = 5
B = -3
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Cheers,
Stan H.
Reply to stanbon@comcast.net or algebra.com
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