Simplify each rational expression. (x^2+10 x)/(2 x^2-5 x) |...

Name: Problem 27, Chapter 6: Intermediate Algebra for College Students
Uploaded: 2022-02-08T02:57:29-08:00
Duration: 43 s
Channel: Victor Salazar
Description: Simplify each rational expression. (x^2+10 x)/(2 x^2-5 x)

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

Cancellation of Common Factors

Once both the numerator and denominator are factored, any factors that appear in both can be canceled. This reduction is valid as long as the values that would zero these factors are excluded from the domain, ensuring the expression remains defined.

Domain Restrictions

When simplifying rational expressions, it is important to consider which values of the variable would make the original denominator zero. These values must be excluded from the domain, as division by zero is undefined in mathematics.

Rational Expression Simplification

This concept involves rewriting a ratio of two polynomials in a simpler form. The process typically includes factoring both the numerator and the denominator completely and then reducing the expression by canceling common factors, provided they are not equal to zero.

Factoring Polynomials

Factoring polynomials is the process of decomposing a polynomial into a product of simpler polynomials. This technique is essential for simplifying expressions and solving equations, as it can reveal underlying structures that allow for cancellation or further manipulation.

Please give Ace some feedback