Simplify each rational expression. (15 x-10)/(8-12 x) |...

Name: Problem 30, Chapter 6: Intermediate Algebra for College Students
Uploaded: 2022-02-27T23:56:34-08:00
Duration: 37 s
Channel: Erika Bustos
Description: Simplify each rational expression. (15 x-10)/(8-12 x)

Key Concepts

Rational Expressions

A rational expression is a fraction in which both the numerator and the denominator are polynomials. Simplifying these expressions involves reducing them to their simplest form by factoring and canceling common factors, all while keeping in mind the restrictions placed on the variables by the denominator.

Factoring Polynomials

Factoring involves rewriting a polynomial as a product of simpler polynomials or constants. This process is crucial in simplifying rational expressions because it reveals common factors in the numerator and denominator that can be canceled.

Common Factor Extraction

Extracting common factors is the process of identifying and factoring out coefficients or variable terms that appear in every term of a polynomial. This step often makes it easier to see further opportunities for cancellation with factors in the denominator.

Cancellation of Common Factors

Once common factors have been factored out of both the numerator and the denominator, they can be canceled, provided that the factors are not equal to zero. This cancellation is the main step in reducing a rational expression to its simplest form.

Domain Restrictions

When simplifying rational expressions, it is important to consider domain restrictions. Any value that makes the original denominator zero must be excluded from the solution set since division by zero is undefined.

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