Write the partial fraction decomposition of the rational expression. + 9x + 14 x+9x+14 (Simplify your answer. Use integers or fractions for any numbers in the expression.)
Write the partial fraction decomposition of the rational expression. + 9x + 14 x+9x+14 (Simplify your answer. Use integers or fractions for any numbers in the expression.)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Partial Fraction Decomposition of a Rational Expression**
**Objective:**
Write the partial fraction decomposition of the given rational expression.
**Expression to Decompose:**
\[
\frac{x}{x^2 + 9x + 14}
\]
**Steps:**
1. **Factor the Denominator**:
- First, factor the quadratic expression \(x^2 + 9x + 14\).
2. **Set Up Partial Fractions**:
- Express the fraction as a sum of simpler fractions with unknown coefficients.
3. **Solve for Coefficients**:
- Use algebra to solve for the unknown coefficients.
**Expression Result:**
\[
\frac{x}{x^2 + 9x + 14} = \text{(Partial fractions with integers or fractions)}
\]
*(Simplify your answer. Use integers or fractions for any numbers in the expression.)*
**Additional Resources:**
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Transcribed Image Text:**Partial Fraction Decomposition of a Rational Expression**
**Objective:**
Write the partial fraction decomposition of the given rational expression.
**Expression to Decompose:**
\[
\frac{x}{x^2 + 9x + 14}
\]
**Steps:**
1. **Factor the Denominator**:
- First, factor the quadratic expression \(x^2 + 9x + 14\).
2. **Set Up Partial Fractions**:
- Express the fraction as a sum of simpler fractions with unknown coefficients.
3. **Solve for Coefficients**:
- Use algebra to solve for the unknown coefficients.
**Expression Result:**
\[
\frac{x}{x^2 + 9x + 14} = \text{(Partial fractions with integers or fractions)}
\]
*(Simplify your answer. Use integers or fractions for any numbers in the expression.)*
**Additional Resources:**
- **Help me solve this**
- **View an example**
- **Get more help**
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