Question

Solve. For Exercises 83 and $84,$ see the second Concept Check in this section, for Exercises 85 and $86,$ see the third Concept Check. Which of the expressions are equivalent to $\frac{x}{5-x} ?$ a. $\frac{-x}{5-x}$ b. $\frac{-x}{-5+x}$ c. $\frac{x}{x-5}$ d. $\frac{-x}{x-5}$

Name: Problem 83, Chapter 6: Intermediate Algebra
Uploaded: 2020-07-16T21:31:46-08:00
Duration: 1 min 10 s
Channel: Amy Jiang
Description: Solve. For Exercises 83 and 84, see the second Concept Check in this section, for Exercises 85 and 86, see the third Concept Check. Which of the expressions are equivalent to (x)/(5-x) ? a. (-x)/(5-x) b. (-x)/(-5+x) c. (x)/(x-5) d. (-x)/(x-5)

   Solve. For Exercises 83 and $84,$ see the second Concept Check in this section, for Exercises 85 and $86,$ see the third Concept Check.
Which of the expressions are equivalent to $\frac{x}{5-x} ?$
a. $\frac{-x}{5-x}$
b. $\frac{-x}{-5+x}$
c. $\frac{x}{x-5}$
d. $\frac{-x}{x-5}$

Intermediate Algebra

Elayn Martin-Gay 6th Edition

Chapter 6, Problem 83

Instant Answer

Solved by Expert Amy Jiang

07/16/2020

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Step 1: First, we need to compare each expression with the given expression $\frac{x}{5-x}$. Show more…

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Solve. For Exercises 83 and $84,$ see the second Concept Check in this section, for Exercises 85 and $86,$ see the third Concept Check. Which of the expressions are equivalent to $\frac{x}{5-x} ?$ a. $\frac{-x}{5-x}$ b. $\frac{-x}{-5+x}$ c. $\frac{x}{x-5}$ d. $\frac{-x}{x-5}$

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Key Concepts

Multiplying by -1 (Sign Manipulation)

Multiplying the numerator and the denominator of a rational expression by -1 does not change its value. This property is essential in simplifying and recognizing that expressions with reversed term orders or signs in the numerator and denominator are equivalent.

Rational Expressions

Rational expressions are fractions where both the numerator and the denominator are polynomials. They require careful consideration of domains, common factors, and the potential for simplification through algebraic manipulation.

Equivalent Expressions

Two expressions are considered equivalent if they have the same value for all values within their common domain. Understanding equivalence involves using operations such as factoring, canceling terms, and simplifying expressions to reveal identical forms.

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