Question

Simplify each rational expression. $$ \frac{x y-y w+x z-z w}{x y+y w+x z+z w} $$

Name: Problem 46, Chapter 6: Intermediate Algebra for College Students
Uploaded: 2020-06-20T23:29:45-08:00
Duration: 1 min 6 s
Channel: Ashley Volpe
Description: Simplify each rational expression. (x y-y w+x z-z w)/(x y+y w+x z+z w)

   Simplify each rational expression.
$$
\frac{x y-y w+x z-z w}{x y+y w+x z+z w}
$$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 6, Problem 46

Instant Answer

Solved by Expert Ashley Volpe

06/20/2020

Step 1

Numerator: Factor out a common "y" from the first two terms and a common "z" from the last two terms. $$ y(x - w) + z(x - w) $$ Denominator: Factor out a common "y" from the first two terms and a common "z" from the last two terms. $$ y(x + w) + z(x + w) $$ Show more…

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Simplify each rational expression. $$ \frac{x y-y w+x z-z w}{x y+y w+x z+z w} $$

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Key Concepts

Simplification of Rational Expressions

Simplification of rational expressions is the process of reducing a fraction where both the numerator and the denominator are algebraic expressions. This is done by factoring both parts and then canceling any common factors, provided they are non-zero, to obtain a simpler, equivalent expression.

Grouping

Grouping in algebra involves arranging terms in an expression in such a way that common factors can be identified and factored out. This approach simplifies complex expressions and often leads to further factorization, streamlining the simplification process.

Factorization

Factorization is the process of rewriting an algebraic expression as a product of simpler expressions or factors. This technique is fundamental in algebra for simplifying expressions and solving equations, as it reveals underlying common elements or simpler constituent parts of a given expression.

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