Problem 45
Question
Explain what is meant by the partial fraction decomposition of a rational expression.
Step-by-Step Solution
Verified Answer
Partial fraction decomposition of a rational expression means expressing a complex fraction as a sum of fractions with simpler denominators for easier computation.
1Step 1: Understanding Rational Expressions
A rational expression is a fraction in which both the numerator and the denominator are polynomials. For example, \(\frac{x^2 - 4x + 3}{x^2 - x - 2}\) is a rational expression.
2Step 2: Defining Partial Fraction Decomposition
Partial fraction decomposition refers to the process of expressing the fraction as a sum of fractions with simpler denominators. In this way, complex rational expressions can be simplified for easier computation.
3Step 3: Example of Partial Fraction Decomposition
For instance, the previous rational expression can be decomposed as follows: \(\frac{x^2 - 4x + 3}{x^2 - x - 2} = \frac{2}{x - 2} - \frac{1}{x + 1}\), demonstrating the partial fraction decomposition.
Other exercises in this chapter
Problem 44
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Let \(x\) represent one number and let \(y\) represent the other number. Use the given conditions to write a system of nonlinear equations. Solve the system and
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