Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 25a

Chapter 1, Problem 25a

Write each rational expression in lowest terms. 8k + 16 / 9k + 18

Verified step by step guidance

Identify the numerator and denominator of the rational expression: numerator is \(8k + 16\) and denominator is \(9k + 18\).

Factor out the greatest common factor (GCF) from the numerator: \(8k + 16 = 8(k + 2)\).

Factor out the greatest common factor (GCF) from the denominator: \(9k + 18 = 9(k + 2)\).

Rewrite the rational expression using the factored forms: \(\frac{8(k + 2)}{9(k + 2)}\).

Cancel the common factor \((k + 2)\) from numerator and denominator, assuming \(k \neq -2\), to simplify the expression to \(\frac{8}{9}\).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Rational Expressions

A rational expression is a fraction where both the numerator and denominator are polynomials. Simplifying rational expressions involves factoring and reducing common factors, similar to simplifying numerical fractions.

Factoring Polynomials

Factoring involves rewriting a polynomial as a product of its factors. Common techniques include factoring out the greatest common factor (GCF), which is essential for simplifying expressions by canceling common terms.

Simplifying Rational Expressions

To simplify a rational expression, factor both numerator and denominator completely, then cancel any common factors. This process reduces the expression to its lowest terms, making it easier to work with or interpret.

Recommended video:

Guided course

05:07

Simplifying Algebraic Expressions

Related Practice

Textbook Question

Multiply or divide as indicated. Write answers in lowest terms as needed. (4/5)∙(6/7)

views

Textbook Question

Use set notation, and list all the elements of each set. {x | x is a natural number not greater than 4}

views

Textbook Question

Simplify each expression. Assume all variables represent nonzero real numbers. (-2x⁵)⁵

Textbook Question

If the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radical form, write it in exponential form. Assume all variables represent positive real numbers. -12x^1/2

views

Textbook Question

Use set notation, and list all the elements of each set. {x | x is a natural number greater than 8 and less than 15}

views

Textbook Question

Multiply or divide as indicated. Write answers in lowest terms as needed. (5/9)∙(2/7)

views