Write each rational expression in lowest terms. (2 x y+2 x w+y+w)/(2 x y+y-2 x w-w)

Name: Problem 50, Chapter 7: Intermediate Algebra
Uploaded: 2020-07-27T16:48:38-08:00
Duration: 1 min 37 s
Channel: James Kiss
Description: Write each rational expression in lowest terms. (2 x y+2 x w+y+w)/(2 x y+y-2 x w-w)

step 1 We have 2xy plus 2x w plus y plus w over 2xy plus y plus y plus y minus 2x w minus w. We need to

Write each rational expression in lowest terms. (2 x y+2 x...

Key Concepts

Rational Expressions

A rational expression is a fraction where both the numerator and the denominator are polynomials. Understanding how to work with these expressions is fundamental in algebra, especially when simplifying, adding, subtracting, multiplying, or dividing them. Simplification involves reducing the expression by canceling out common factors between the numerator and the denominator.

Polynomial Factoring

Factoring polynomials involves rewriting a polynomial as a product of its factors. This may include common factor extraction, factoring by grouping, and applying special factoring formulas such as the difference of squares. Being adept at polynomial factoring is critical when simplifying rational expressions, as it helps to reveal common factors.

Factoring by Grouping

Factoring by grouping is a technique used when a polynomial has four or more terms. It involves grouping terms into subsets that have a common factor and then factoring out these common factors from each group. This method can simplify complex expressions and is particularly useful when a polynomial does not factor easily through other methods.

Cancellation of Common Factors

Cancellation of common factors is the process of dividing both the numerator and the denominator of a rational expression by the same non-zero polynomial factor. This step reduces the rational expression to its lowest terms. It is imperative to ensure that the factors being canceled are indeed common to both the numerator and the denominator and that any restrictions on the variable (to avoid division by zero) are noted.

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