Math Example--Rational Concepts--Rational Expressions: Example 17

Topic

Rational Expressions

Description

This example demonstrates how to combine the rational expressions 1 / (x - 9) - 1 / 10. The solution involves finding a common denominator, which is 10(x - 9), and then subtracting the fractions to get (-x + 19) / (10(x - 9)). We multiply each fraction by the appropriate factor to create equivalent fractions with the common denominator: (1 * 10) / ((x - 9) * 10) - (1 * (x - 9)) / (10 * (x - 9)) = 10 / (10(x - 9)) - (x - 9) / (10(x - 9)). Then, we subtract the numerators while keeping the common denominator: (10 - (x - 9)) / (10(x - 9)) = (19 - x) / (10(x - 9)) = (-x + 19) / (10(x - 9)).

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 denominators, including both constants and linear expressions. 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 subtracting a constant fraction from a fraction with a linear expression in the denominator. Notice how we find the common denominator and perform the subtraction. Can you explain why the result has a negative x term in the numerator?

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