Math Example--Rational Concepts--Rational Expressions: Example 9

Topic

Rational Expressions

Description

This example illustrates how to combine the rational expressions 1/(2x) + 1/(5x). The solution involves finding a common denominator, which is 10x, and then adding the fractions to get 7/(10x). We multiply each fraction by the appropriate unit fraction to create equivalent fractions with the common denominator: (1 * 5)/(2x * 5) + (1 * 2)/(5x * 2) = 5/(10x) + 2/(10x). Then, we add the numerators while keeping the common denominator: (5 + 2)/(10x) = 7/(10x).

Rational expressions are a crucial 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 similar variable denominators. By working through these examples, students learn to identify least common denominators and perform the necessary operations to simplify the expressions.

Exposure to multiple worked-out examples is essential for students to develop a deep 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 advanced algebraic situations.

Teacher's Script: In this example, we're adding fractions with similar denominators, both containing the variable x. Notice how we find the least common denominator. Can you explain why 10x is the least common denominator for 2x and 5x?

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