It's a rational expression you divide the top fraction by the bottom ### Division of Rational ExpressionsTo divide the given rational expressions, follow these steps:#### Problem:\[\frac{x^2 + 10x + 25}{x^2 - 25} \div \frac{x^2 - 2x - 35}{x^2 - 12x + 35}\]#### Method:1. **Rewrite as Multiplication**: To divide fractions, multiply by the reciprocal of the divisor. \[ \frac{x^2 + 10x + 25}{x^2 - 25} \times \frac{x^2 - 12x + 35}{x^2 - 2x - 35} \]2. **Factor Each Quadratic Expression**: **Numerator of the First Fraction:** \[ x^2 + 10x + 25 = (x + 5)(x + 5) \] **Denominator of the First Fraction:** \[ x^2 - 25 = (x + 5)(x - 5) \] **Numerator of the Second Fraction:** \[ x^2 - 12x + 35 = (x - 7)(x - 5) \] **Denominator of the Second Fraction:** \[ x^2 - 2x - 35 = (x - 7)(x + 5) \]3. **Substitute the Factors Back**: \[ \frac{(x + 5)(x + 5)}{(x + 5)(x - 5)} \times \frac{(x - 7)(x - 5)}{(x - 7)(x + 5)} \]4. **Cancel Common Factors**: After canceling common factors, the expression simplifies to: \[ \frac{(x + 5)}{(x - 5)} \]5. **Simplify Your Answer:** The simplified expression is: \[ \frac{x + 5}{x - 5} \]Remember, always check for values that make the original denominators zero to identify any restrictions on the variables.

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Answered: ← Divide. x² +10x+25 ²-25 x² - 2x-35 x²…

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Algebra

← Divide. x² +10x+25 ²-25 x² - 2x-35 x² - 12x+35 x² + 10x + 25 x2-25 x² - 2x-35 x²-12x+35 (Simplify your answer.) ww

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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