Question

Explain the closure property as it relates to rational expressions. Give an example and simplify it to prove closure.

Options:
1. The closure property states that the sum or product of any two rational expressions will always result in a rational expression.
2. The closure property states that the sum or product of any two rational expressions may or may not result in a rational expression.
3. The closure property states that the sum or product of any two rational expressions will never result in a rational expression.
4. The closure property states that the sum or product of any two rational expressions is undefined.

Answer 1

The closure property states that the sum or product of any two rational expressions will always result in a rational expression. Addition or multiplication of rational expressions will yield another rational expression. Hence, 1) is correct.

Step-by-step explanation:

The closure property as it relates to rational expressions states that the sum or product of any two rational expressions will always result in a rational expression. This means that if we add or multiply two rational expressions, the result will also be a rational expression.

For example, let's consider the rational expressions 2/3 and 4/5. To find the sum of these expressions, we need to find a common denominator, which is 15 in this case. We then add the numerators to get (2 * 5 + 4 * 3)/15 = 22/15, which is a rational expression.

Similarly, if we multiply these expressions, we get (2/3) * (4/5) = (2 * 4)/(3 * 5) = 8/15, which is also a rational expression. These examples demonstrate the closure property of rational expressions.