Write the rational expression in simplest form. (x^2-9)/(x^3+x^2-9 x-9)

Name: Problem 44, Chapter 0: College Algebra: Real Mathematics, Real People
Uploaded: 2021-03-03T05:33:09-08:00
Duration: 2 min 52 s
Channel: Matthew Biollo
Description: Write the rational expression in simplest form. (x^2-9)/(x^3+x^2-9 x-9)

step 1 This problem involves factoring and in order to simplify rational expression. So we're going to

Write the rational expression in simplest form....

Key Concepts

Common Factor Cancellation

After factorizing both the numerator and the denominator in a rational expression, common factors can often be canceled. This cancellation is the step that simplifies the expression to its lowest terms, but it must be done carefully to avoid losing critical information, such as restrictions on the domain.

Factor by Grouping

Factor by grouping is a method used to factor polynomials, usually those with four or more terms. The process involves grouping terms that share common factors, factoring each group, and then factoring out the common binomial factor. This technique is especially useful when the polynomial does not have an obvious common factor throughout.

Rational Expressions

A rational expression is a fraction in which both the numerator and the denominator are polynomials. Simplification involves rewriting the expression as a product of factors and canceling any common factors, while ensuring that the restrictions on the variable (where the denominator is zero) are maintained.

Factoring Polynomials

Factoring polynomials involves expressing a polynomial as a product of simpler polynomials. This process is crucial for simplifying rational expressions because it reveals common factors in the numerator and denominator which can be canceled, simplifying the expression.

Difference of Squares

The difference of squares is a specific factoring technique used when a polynomial can be written as the difference of two perfect squares. Using the identity a² - b² = (a - b)(a + b), this approach allows for easy factorization of certain quadratic expressions.

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