Math Example--Rational Concepts--Rational Expressions: Example 3

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1/x + 1/3. The solution involves finding a common denominator, which is 3x, and then adding the fractions to get (x + 3)/3x. We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 3/3) + (1 * x/x) = 3/(3x) + x/(3x). Then, we add the numerators while keeping the common denominator: (3 + x)/(3x) = (x + 3)/(3x).

Rational expressions are a fundamental concept in algebra, representing the ratio of two polynomials. This collection of examples helps teach the topic by presenting various scenarios where students must combine rational expressions with both numeric and variable terms. By working through these examples, students learn to identify common denominators and perform the necessary operations to simplify the expressions, even when variables are involved.

Exposure to multiple worked-out examples is essential for students to develop a comprehensive understanding of rational expressions. Each example builds upon previous knowledge while introducing new challenges, helping students recognize patterns and develop problem-solving strategies that can be applied to more complex algebraic situations.

Teacher's Script: Now we're dealing with a variable in one of our fractions. Notice how we still follow the same steps to find a common denominator and combine the terms. Can you explain why the common denominator is 3x in this case?

For a complete collection of math examples related to Rational Expressions click on this link: Math Examples: Rational Expressions Collection.