Solving Partial Fractions: Finding Unknown Coefficients

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Discussion Overview

The discussion revolves around solving a partial fractions problem involving the integration of the expression (8x-17)/(x^2+x-12). Participants are attempting to find the unknown coefficients A and B in the equation and are comparing their results with those provided in a textbook.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant presents the problem and sets up the equations A+B = 8 and 4B-3A = -17 based on their interpretation of the partial fractions decomposition.
  • Another participant suggests that the discrepancy may arise from differing definitions of A and B, implying that the approach could still yield the correct answer.
  • A participant points out that their calculated values for A and B differ from those in the book, stating they found B = 41/7 and A = 15/7, while the book claims B = 7 and A = 1.
  • Another participant challenges the validity of the values provided by the original poster, indicating that those values do not satisfy the equations derived.
  • A later reply proposes an alternative method to find A and B by substituting specific values of x into the equation, suggesting that this method leads to A = 7 and B = 1.

Areas of Agreement / Disagreement

Participants express disagreement regarding the values of A and B, with multiple competing views on the correct approach to solving the problem. The discussion remains unresolved as participants have not reached a consensus on the correct coefficients.

Contextual Notes

There is a lack of clarity regarding the definitions of A and B, and the assumptions made in setting up the equations. The participants' methods for solving the equations also vary, leading to different results.

PrudensOptimus
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hi, the problem is:


∫ (8x-17)/x^2+x-12 dx = ∫ .../(x+4)(x-3) dx

so 8x - 17 = A(x-3) + B(x+4)

(A+B)x + 4B - 3A

so we have 2 eq and 2 unknown

A+B = 8
4B-3A = -17

... but the book says it's suppose to be 4A - 3B,.. I don't know what I did wrong.

Please help.
 
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They probably just defined A and B differently than you did. (They must have said (8x-17)/(x2+x-12) = A/(x-3) + B/(x+4) ). You'll still get the right answer your way.
 
the ending result is different...

they got B = 7 and A = 1...


I got B = 41/7, and A = 15/7
 
Well, the B and A you listed aren't solutions to the equations you got...
 
Originally posted by PrudensOptimus
(A+B)x + 4B - 3A

so we have 2 eq and 2 unknown

A+B = 8
4B-3A = -17

You don't have to solve these like that.

so 8x - 17 = A(x-3) + B(x+4)

Starting from here, just plug in x=+3 and x=-4.

x=3:
8(3)-17=A(3-3)=B(3+4)
7=7B
B=1

x=-4:
8(-4)-17=A(-4-3)+B(-4+4)
-49=-7A
A=7
 
amazing.
 

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