Math Example--Rational Concepts--Rational Expressions: Example 22

Topic

Rational Expressions

Description

This example illustrates how to combine the rational expressions 1 / (x - 5) + 1 / (x - 4). The solution involves finding a common denominator, which is (x - 5)(x - 4), and then adding the fractions to get (2x - 9) / (x² - 9x + 20). We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * (x - 4)) / ((x - 5) * (x - 4)) + (1 * (x - 5)) / ((x - 4) * (x - 5)) = (x - 4) / (x² - 9x + 20) + (x - 5) / (x² - 9x + 20). Then, we add the numerators while keeping the common denominator: ((x - 4) + (x - 5)) / (x² - 9x + 20) = (2x - 9) / (x² - 9x + 20).

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 different linear denominators. By working through these examples, students learn to identify 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 two fractions with similar linear expressions in the denominators. Notice how we find the common denominator. Can you explain why the constant term in the numerator of the final expression is -9?

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