Question

Explain what is meant by the least common denominator of two rational expressions.

Short answer

The Least Common Denominator of two rational expressions is the Least Common Multiple of their respective denominators and is used to simplify operations like addition or subtraction of rational expressions.

Step-by-step solution

Concept of Rational Expression

A rational expression refers to a ratio of two polynomial expressions. It's similar to a fraction, with the denominator and numerator being polynomials.

Understanding the Denominator

In the rational expression, the denominator is the bottom part. When dealing with two or more rational expressions, each will have its own denominator.

Definition of Least Common Denominator (LCD)

The least common denominator (LCD) can be defined as the least common multiple (LCM) of the denominators of two or more fractions or rational expressions.

Use of LCD in Rational Expressions

When you have two rational expressions, finding the LCD simplifies the process of adding, subtracting, or comparing the expressions. It's akin to finding the LCD of fractions to align them for similar operations.

Calculation of LCD

You can calculate the LCD by factoring the denominators and multiplying each factor the greatest number of times it occurs in either denominator. The result is the smallest expression which both denominators divide evenly into, hence it's the Least Common Denominator.