Solve each rational equation. (2)/(x-2)+(4)/(x)=2

Name: Problem 34, Chapter 7: Introductory Algebra for College Students
Uploaded: 2021-02-13T11:16:45-08:00
Duration: 3 min 26 s
Channel: Priyanka Sadarangani
Description: Solve each rational equation. (2)/(x-2)+(4)/(x)=2

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

Rational Equations

A rational equation is an equation that involves fractions whose numerators and/or denominators contain algebraic expressions. The process of solving a rational equation typically includes finding a common denominator, eliminating the fractions, and then solving the resulting equation.

Domain Restrictions

Domain restrictions refer to the conditions that must be met for a rational expression to be defined, primarily ensuring that the denominators are not equal to zero. In any rational equation, it is important to determine the values that make any denominator zero, as these values are not permitted in the solution set.

Clearing Denominators

Clearing denominators is a technique used to eliminate fractions from an equation by multiplying every term by the least common denominator (LCD). This method simplifies the equation into a polynomial form, making it easier to solve, but it requires careful consideration of domain restrictions to avoid introducing extraneous solutions.

Extraneous Solutions

Extraneous solutions are results obtained after manipulating the equation (such as by clearing denominators) that do not satisfy the original equation. It is crucial to substitute any potential solutions back into the original equation to ensure they do not fall into the restricted domain or generate undefined expressions.

Transcript

Please give Ace some feedback