Question

What is the closure property of subtraction for rational expressions? Explain why rational expressions are closed under subtraction.

Answer 1

I already answered this question by saying that the closure property of susbtraction for rational expression is the fact that the result of the substraction of rational expression is also a rational expression.


The closure property applies to many operations and to many sets. It means that the application of a particular operation on a particular set will result in an element of the same set.

In this case of substraction it means that when substraction is performed to the set any elements in the rational set the result will we also an element of the rational set.

So, rational expressions are closed under subtraction becasue always that you subract a rational from another rational (or even the same rational) the result is also a rational.

Here are some new examples which will help you:

1/2 - 1/4 = 1/4

100/3 - 50/3 = 50/3

2.276 - 1.325 = 0.951

That is if you subtract a rational from a rational the result is a rational (always). You can not escape from rational set by subtracting elements of the same set.

Again, always that you subtract a rational from other rational the result is a rational.

Answer 2

The closure property of multiplication for rational expressions states that the product of two rational expressions is a rational expression. Since the variable in a rational expression just represents a number, and the closure property holds true for multiplication of rational numbers, it also holds true for multiplication of rational expressions for values for which the expressions are defined.