3 -2 Find the least common denominator of and 2 - 4 2 х- 8х — 33

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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#### Rational Expressions: Finding the LCD of Rational Expressions with Quadratic Denominators

To find the least common denominator (LCD) of the rational expressions \(\frac{3}{x^2 - 8x - 33}\) and \(\frac{-2}{x^2 - 4}\), follow these steps:

1. **Factor each quadratic expression:**
   - \(x^2 - 8x - 33\) factors into \((x - 11)(x + 3)\)
   - \(x^2 - 4\) factors into \((x - 2)(x + 2)\)

2. **Identify the Least Common Denominator (LCD):**
   - The LCD must include each factor that appears in any of the denominators.
   - The denominators are: \((x - 11)(x + 3)\) and \((x - 2)(x + 2)\)
   - Therefore, the LCD is \((x - 11)(x + 3)(x - 2)(x + 2)\)

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Transcribed Image Text:#### Rational Expressions: Finding the LCD of Rational Expressions with Quadratic Denominators To find the least common denominator (LCD) of the rational expressions \(\frac{3}{x^2 - 8x - 33}\) and \(\frac{-2}{x^2 - 4}\), follow these steps: 1. **Factor each quadratic expression:** - \(x^2 - 8x - 33\) factors into \((x - 11)(x + 3)\) - \(x^2 - 4\) factors into \((x - 2)(x + 2)\) 2. **Identify the Least Common Denominator (LCD):** - The LCD must include each factor that appears in any of the denominators. - The denominators are: \((x - 11)(x + 3)\) and \((x - 2)(x + 2)\) - Therefore, the LCD is \((x - 11)(x + 3)(x - 2)(x + 2)\) The respective input box is provided for the user to type their answer, and clarification buttons are available to explain/further illustrate the problem: - **[ ]** (Input box for the user to type the answer) - **[∓]** (Button for switching the answer form, such as positive/negative signs) - **[⟳]** (Button for resetting the input) - **[?]** (Button for getting hints or help)
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