Subtraction of Rational Expressions

Definition

Subtraction of rational expressions involves finding the difference between two or more rational expressions. This operation is essential in the context of adding and subtracting rational expressions with a common denominator or with unlike denominators, as covered in Sections 8.3 and 8.4 of the curriculum.

5 Must Know Facts For Your Next Test

1. To subtract rational expressions with a common denominator, you subtract the numerators and keep the common denominator.
2. When subtracting rational expressions with unlike denominators, you must first find the least common multiple (LCM) of the denominators to create a common denominator.
3. After finding the common denominator, you can subtract the numerators and keep the common denominator.
4. Subtracting rational expressions may result in a rational expression with a numerator that is a polynomial and a denominator that is a polynomial.
5. The subtraction of rational expressions follows the same rules and properties as the subtraction of fractions with numerical values.

Review Questions

• Explain the process of subtracting rational expressions with a common denominator.
  • To subtract rational expressions with a common denominator, you first identify the common denominator, which is the least common multiple (LCM) of the denominators. Then, you subtract the numerators of the rational expressions while keeping the common denominator. The resulting expression will be a rational expression with the same common denominator.
• Describe the steps involved in subtracting rational expressions with unlike denominators.
  • When subtracting rational expressions with unlike denominators, you must first find the least common multiple (LCM) of the denominators to create a common denominator. Once the common denominator is established, you can then subtract the numerators and keep the common denominator. This process ensures that the resulting expression is a valid rational expression that can be simplified further if necessary.
• Analyze how the subtraction of rational expressions is similar to the subtraction of numerical fractions, and explain any key differences.
  • The subtraction of rational expressions follows the same general principles as the subtraction of numerical fractions. In both cases, you subtract the numerators while keeping the common denominator. However, the key difference is that in the case of rational expressions, the numerators and denominators are polynomials, rather than just numerical values. This added complexity requires additional steps, such as finding the least common multiple of the denominators, to ensure the resulting expression is a valid rational expression.

Related terms

Rational Expression:

A rational expression is a quotient of two polynomials, where the denominator is not equal to zero.

Common Denominator:

The common denominator is the least common multiple (LCM) of the denominators of the rational expressions being added or subtracted.

Unlike Denominators:

Rational expressions with unlike denominators have denominators that are not the same, and therefore, cannot be directly added or subtracted without first finding a common denominator.