Method of equating coefficients

Definition

The method of equating coefficients is a technique used to determine the values of unknown constants in an algebraic expression by matching corresponding coefficients on both sides of an equation. This method is often employed in the context of integrating rational functions using partial fractions.

5 Must Know Facts For Your Next Test

1. The method of equating coefficients is critical for solving systems of equations that arise in partial fraction decomposition.
2. It involves setting up and solving a system of linear equations based on matching the powers of $x$ on both sides.
3. This technique helps find the constants in expressions like $\frac{A}{x-1} + \frac{B}{x+2}$ when decomposing rational functions.
4. Equating coefficients requires expanding polynomial expressions and combining like terms before setting up equations.
5. It’s essential to correctly align terms with corresponding powers to avoid errors in solving for constants.

Review Questions

• How do you use the method of equating coefficients to find unknown constants in partial fraction decomposition?
• Why is it important to match corresponding powers when using this method?
• What are the steps involved in setting up equations when using equating coefficients?

Related terms

Partial Fraction Decomposition: A technique used to break down a complex rational function into simpler fractions that are easier to integrate.

Rational Function: A function represented by the ratio of two polynomials.

Integration by Substitution: A method for finding integrals where one substitutes part of the integral with a new variable to simplify integration.