Reduce each rational expression to lowest terms. (3 y^2-y-2)/(3 y^2+5 y+2)

Name: Problem 14, Chapter 0: College Algebra
Uploaded: 2020-05-09T19:17:23-08:00
Duration: 1 min 35 s
Channel: Brittany Scott
Description: Reduce each rational expression to lowest terms. (3 y^2-y-2)/(3 y^2+5 y+2)

step 1 Okay, we're looking into simplifying this expression. With that top term of 3y squared minus y,

Reduce each rational expression to lowest terms. (3...

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Key Concepts

Polynomial Factoring

Polynomial factoring is the process of expressing a polynomial as a product of its simpler, irreducible factors. This technique is fundamental when simplifying rational expressions, as it reveals common factors that can be canceled between the numerator and the denominator.

Factoring Quadratic Polynomials

Quadratic polynomials, which are second-degree polynomials, can often be broken down into a product of two binomials. Techniques such as splitting the middle term or using the quadratic formula help factor these polynomials. This factorization is crucial for simplifying rational expressions that involve quadratic terms.

Rational Expressions

Rational expressions are fractions where both the numerator and the denominator are polynomials. Simplifying these expressions involves reducing them to their lowest terms by identifying common factors in the numerator and denominator and canceling them, while being mindful of restrictions that prevent division by zero.

Cancellation of Common Factors

Once both the numerator and the denominator have been factored, any common factors can be canceled, simplifying the rational expression to its lowest terms. It is important to note that canceling is valid only when these factors are not equal to zero, ensuring the expression remains defined.

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