College Algebra

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Decomposition

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College Algebra

Definition

Decomposition involves breaking down a complex fraction into simpler partial fractions. This is often used to simplify integration or solve algebraic equations more easily.

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5 Must Know Facts For Your Next Test

  1. Partial fraction decomposition is particularly useful for integrating rational functions.
  2. To decompose a fraction, the degree of the numerator must be less than the degree of the denominator.
  3. If the denominator has repeated linear factors, each factor must have a separate term in the decomposition.
  4. For irreducible quadratic factors in the denominator, use terms with linear numerators in the decomposition.
  5. Decomposition requires solving a system of equations to determine the coefficients of the partial fractions.

Review Questions

  • What conditions must be met for a rational function to be decomposed into partial fractions?
  • How do you handle repeated linear factors when performing partial fraction decomposition?
  • Describe how to decompose a rational function with an irreducible quadratic factor in its denominator.
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