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x + 9 x² – 8x Find:

x + 9 x² – 8x Find:

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Multiplying Rational Expressions #### Problem: Find: \[ \left( \frac{x^2 + x - 1}{2x + 3} \right)^2 \] #### Solution: We will find the product: \[ \left( \frac{x^2 + x - 1}{2x + 3} \right) \left( \frac{x^2 + x - 1}{2x + 3} \right) \] using the rule for multiplying rational expressions. The exponent 2 means the base, \[ \frac{x^2 + x - 1}{2x + 3} \] should be written as a factor two times. \[ \left( \frac{x^2 + x - 1}{2x + 3} \right)^2 = \left( \frac{x^2 + x - 1}{2x + 3} \right) \left( \frac{x^2 + x - 1}{2x + 3} \right) \] \[ = \frac{(x^2 + x - 1)(x^2 + x - 1)}{(2x + 3)(2x + 3)} \] \[ = \frac{x^4 + 2x^3 - x^2 - 2x + 1}{4x^2 + 12x + 9} \] 1. **Multiply the numerators:** \((x^2 + x - 1)(x^2 + x - 1) = x^4 + 2x^3 - x^2 - 2x + 1\) 2. **Multiply the denominators:** \((2x + 3)(2x + 3) = 4x^2 + 12x + 9\) #### Practice Problem: Find: \[ \left( \frac{x + 9}{x^2 - 8x} \right)^2 \] ### Explanation of Terms and Steps: 1. **Identify the base expression:** Identify and write the expression being squared. 2. **Factor the base expression:** Write the base expression as two factors. 3. **Apply the multiplication rule:** Multiply the numerators and denominators separately. 4. **Simplify the expression:** Combine like terms and reduce the expression if possible. This step-by-step approach helps in multiplying rational expressions and understanding
Transcribed Image Text:### Multiplying Rational Expressions #### Problem: Find: \[ \left( \frac{x^2 + x - 1}{2x + 3} \right)^2 \] #### Solution: We will find the product: \[ \left( \frac{x^2 + x - 1}{2x + 3} \right) \left( \frac{x^2 + x - 1}{2x + 3} \right) \] using the rule for multiplying rational expressions. The exponent 2 means the base, \[ \frac{x^2 + x - 1}{2x + 3} \] should be written as a factor two times. \[ \left( \frac{x^2 + x - 1}{2x + 3} \right)^2 = \left( \frac{x^2 + x - 1}{2x + 3} \right) \left( \frac{x^2 + x - 1}{2x + 3} \right) \] \[ = \frac{(x^2 + x - 1)(x^2 + x - 1)}{(2x + 3)(2x + 3)} \] \[ = \frac{x^4 + 2x^3 - x^2 - 2x + 1}{4x^2 + 12x + 9} \] 1. **Multiply the numerators:** \((x^2 + x - 1)(x^2 + x - 1) = x^4 + 2x^3 - x^2 - 2x + 1\) 2. **Multiply the denominators:** \((2x + 3)(2x + 3) = 4x^2 + 12x + 9\) #### Practice Problem: Find: \[ \left( \frac{x + 9}{x^2 - 8x} \right)^2 \] ### Explanation of Terms and Steps: 1. **Identify the base expression:** Identify and write the expression being squared. 2. **Factor the base expression:** Write the base expression as two factors. 3. **Apply the multiplication rule:** Multiply the numerators and denominators separately. 4. **Simplify the expression:** Combine like terms and reduce the expression if possible. This step-by-step approach helps in multiplying rational expressions and understanding
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