perform the indicated operations. (2 n)/(3 n^2-8 n-3)+(1)/(6-2 n)-(3)/(3 n+1)

Name: Problem 86, Chapter 7: Beginning and Intermediate Algebra
Uploaded: 2021-04-06T01:55:12-08:00
Duration: 1 min 52 s
Channel: Erika Bustos
Description: perform the indicated operations. (2 n)/(3 n^2-8 n-3)+(1)/(6-2 n)-(3)/(3 n+1)

step 1 We need to perform the operations on these fractions, but we first need to find a common denomin

Perform the indicated operations. (2 n)/(3 n^2-8...

Key Concepts

Algebraic Simplification

Algebraic simplification refers to reducing an expression to its simplest form by canceling common factors, combining like terms, and eliminating extraneous elements. In the context of rational expressions, this final step ensures that the resulting expression is as concise and clear as possible after performing the indicated operations.

Polynomial Factoring

Polynomial factoring is the process of rewriting a polynomial as a product of simpler polynomials, often of lower degrees. This technique is essential when working with rational expressions because it may reveal common terms that can be canceled or used to construct a common denominator for addition or subtraction.

Rational Expressions

Rational expressions are fractions where both the numerator and the denominator are polynomials. Mastering these expressions involves performing operations such as addition, subtraction, multiplication, and division, which often require manipulation through factoring and simplifying the expressions to combine them effectively.

Finding a Common Denominator

Finding a common denominator involves determining a shared multiple of the denominators in multiple rational expressions. This step is crucial when adding or subtracting these expressions since it allows each fraction to be rewritten with the same denominator, making the arithmetic straightforward.

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