Understanding Rational Expression Operations
This page delves into the intricacies of adding and subtracting rational expressions, providing a thorough explanation of the process and its applications in algebraic problem-solving.
To add or subtract rational expressions, they must have the same denominator. When dealing with expressions that have different denominators, the key is to find a common denominator. The easiest method to achieve this is by multiplying each numerator and denominator by the product of the other denominators.
Definition: A rational expression is an algebraic fraction where both the numerator and denominator are polynomials.
The page presents a general formula for adding rational expressions:
Q(x)/W(x) + P(x)/W(x) = [Q(x)*P(x) + Q(x)*W(x)] / [W(x)*P(x)]
This formula illustrates how to combine two rational expressions with different denominators into a single fraction.
Example: The document provides a specific example of adding two rational expressions:
a = (x + 2) / (x² - 1) and b = 1 / (2x + 1)
The page then poses a series of problems for students to solve:
- Calculate a + b
- Calculate a - b
- Calculate a + b + c
- Calculate a - b + c
These problems are designed to reinforce the concepts of adding and subtracting rational expressions and provide practice in applying the techniques learned.
Highlight: The solution to a + b is worked out in detail, demonstrating the step-by-step process of finding a common denominator and combining the fractions.
The page concludes with more complex examples involving the addition and subtraction of multiple rational expressions, including one with three terms (a + b + c). These examples showcase how to handle more intricate problems and reinforce the importance of maintaining a common denominator throughout the calculations.
Vocabulary:
- Wyrażenia wymierne: Rational expressions
- Wspólny mianownik: Common denominator
- Licznik: Numerator
- Mianownik: Denominator
This comprehensive guide provides students with a solid foundation for solving problems involving rational expressions, preparing them for more advanced algebraic concepts and applications.
