Question

Completely simplify each expression. $$ \frac{5}{x-1}+\frac{3}{1-x} $$

   Completely simplify each expression.
$$
\frac{5}{x-1}+\frac{3}{1-x}
$$

Precalculus : Building Concepts and Connections

Precalculus : Building Concepts and Connections

Revathi Narasimhan 1st Edition

Chapter 6, Problem 7

Instant Answer

Solved by Expert Joshua Eastwood

04/11/2020

Step 1

That is, $1-x = -(x-1)$. Show more…

Show all steps

lock

Thanks for your feedback!

Completely simplify each expression. $$ \frac{5}{x-1}+\frac{3}{1-x} $$

Play audio

Feedback

Powered by NumerAI

Joshua Eastwood and 68 other subject Precalculus educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Sign Factoring

Sign factoring is the technique of factoring out a negative sign from an expression. In the context of simplifying rational expressions, recognizing that expressions like (1 - x) can be written as -(x - 1) is key. This understanding helps in aligning denominators and simplifies the addition or subtraction of fractions.

Common Denominator

To combine rational expressions, it is necessary to rewrite them with a common denominator. This process often involves recognizing that denominators which look different may be equivalent up to a factor (such as a sign change), allowing them to be adjusted so that they can be combined into a single fraction.

Rational Expressions

Rational expressions are fractions where the numerator and/or denominator are polynomials. Simplifying these expressions involves operations like finding a common denominator, factoring, and cancelling common factors while being cautious of domain restrictions.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later