key term - Like Denominators

Definition

Like denominators refer to rational expressions that have the same denominator. This concept is crucial in the context of adding and subtracting rational expressions, as it allows for simplification and combination of fractions with a common denominator.

5 Must Know Facts For Your Next Test

1. When adding or subtracting rational expressions, the denominators must be the same (like denominators) in order to perform the operation.
2. Rational expressions with like denominators can be added or subtracted by adding or subtracting the numerators and keeping the common denominator.
3. Finding the least common denominator (LCD) is a crucial step when dealing with rational expressions with unlike denominators.
4. Simplifying rational expressions with like denominators often involves factoring the numerator and denominator and canceling common factors.
5. Rational expressions with like denominators can be multiplied or divided by simply multiplying or dividing the numerators and keeping the common denominator.

Review Questions

• Explain the importance of having like denominators when adding or subtracting rational expressions.
  • Having like denominators is essential when adding or subtracting rational expressions because it allows the numerators to be combined directly. If the denominators are not the same, the expressions must first be converted to have a common denominator, typically the least common denominator (LCD), before the operation can be performed. This ensures that the resulting expression is in simplified form and maintains the same level of complexity as the original expressions.
• Describe the process of finding the least common denominator (LCD) and how it is used to simplify rational expressions with unlike denominators.
  • The least common denominator (LCD) is the smallest common denominator shared by a set of rational expressions. To find the LCD, you must first identify the prime factors of each denominator, then take the product of the highest power of each prime factor. This LCD is then used to convert the rational expressions to have a common denominator, allowing them to be added, subtracted, multiplied, or divided. By converting the expressions to have the LCD, the resulting expression is in its simplest form and the operations can be performed efficiently.
• Analyze the relationship between simplifying rational expressions and the concept of like denominators.
  • Simplifying rational expressions is closely tied to the concept of like denominators. When the denominators are the same, the process of simplification involves factoring the numerator and denominator, then canceling any common factors. This results in a simplified expression with the same denominator. However, if the denominators are not like, the expressions must first be converted to have a common denominator, typically the LCD, before simplification can occur. The ability to recognize and work with like denominators is essential for effectively simplifying rational expressions and reducing them to their most basic form.

Related terms

Rational Expression:

A rational expression is a fraction where both the numerator and denominator are polynomials.

Least Common Denominator (LCD):

The least common denominator is the smallest common denominator shared by a set of rational expressions.

Simplifying Rational Expressions: The process of reducing a rational expression to its simplest form by factoring the numerator and denominator and canceling common factors.