Calculus question: Partial Fractions

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SUMMARY

The discussion focuses on solving the calculus problem involving partial fractions for the expression (5x^3 + 4x^2 - 4) / (x^3(x + 1)). The user seeks guidance on how to express the equation in the form A/x + B/x^2 + C/x^3 + D/(x + 1). Participants provide insights on setting up the equation correctly, emphasizing the importance of identifying coefficients A, B, C, and D through algebraic manipulation and equating coefficients.

PREREQUISITES
  • Understanding of partial fraction decomposition
  • Familiarity with polynomial long division
  • Basic algebraic manipulation skills
  • Knowledge of solving equations for unknown coefficients
NEXT STEPS
  • Study the method of partial fraction decomposition in detail
  • Practice polynomial long division with various examples
  • Learn how to equate coefficients in algebraic expressions
  • Explore applications of partial fractions in integration techniques
USEFUL FOR

Students studying calculus, particularly those focusing on integration techniques and algebraic manipulation, as well as educators seeking to enhance their teaching methods in partial fractions.

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Homework Statement



(〖5x^3〗+〖4x^2〗-4)/((x^3)(x+1))

Homework Equations



Partial Fractions

The Attempt at a Solution



I know that I need to use partial fractions. But I don't know how to put it in (A/x)+(B/x)...etc

Would someone please kindly show me how to set up this equation? I've been stuck on the same problem for an hour now.
Thanks in advance to those who can shed some light on this!
 
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You want
\frac{5x^3+ 4x^2- 4}{x^3(x+1)}= \frac{A}{x}+ \frac{B}{x^2}+ \frac{C}{x^3}+ \frac{D}{x+ 1}
 

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