In the following exercises, simplify. ((2)/(x+5))/((3)/(x-5)+(1)/(x^2-25))

Name: Problem 279, Chapter 8: Elementary Algebra
Uploaded: 2021-07-20T20:45:32-08:00
Duration: 3 min 5 s
Channel: Katelyn Vandeaver
Description: In the following exercises, simplify. ((2)/(x+5))/((3)/(x-5)+(1)/(x^2-25))

step 1 The first thing that we need to do to simplify this problem is combine those fractions on the bo

In the following exercises, simplify....

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Key Concepts

Fraction Addition and Common Denominator

When adding fractions with different denominators, it's necessary to convert them to equivalent fractions with a common denominator. This method is essential to combine terms accurately, particularly in rational expressions where addition or subtraction of fractions occurs.

Difference of Squares

This is a factoring technique used for expressions of the form a² - b², which can be factored into (a - b)(a + b). Recognizing and applying this concept is crucial in simplifying algebraic expressions and canceling common factors in rational expressions.

Complex Fractions

This concept involves simplifying expressions where fractions appear within a larger fractional structure. It requires rewriting the complex fraction as a simpler expression, often by finding a common denominator or multiplying numerator and denominator by the reciprocal of the inner fraction.

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