Math Example--Rational Concepts--Rational Expressions: Example 23

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1 / (x + 2) - 1 / (x + 6). The solution involves finding a common denominator, which is (x + 2)(x + 6), and then subtracting the fractions to get 4 / (x² + 8x + 12). We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * (x + 6)) / ((x + 2) * (x + 6)) - (1 * (x + 2)) / ((x + 6) * (x + 2)) = (x + 6) / (x² + 8x + 12) - (x + 2) / (x² + 8x + 12). Then, we subtract the numerators while keeping the common denominator: ((x + 6) - (x + 2)) / (x² + 8x + 12) = 4 / (x² + 8x + 12).

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 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 crucial 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: In this example, we're subtracting two fractions with different linear expressions in the denominators. Pay attention to how we find the common denominator and perform the subtraction. Can you explain why the x terms cancel out in the numerator of the final expression?

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