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

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We can show this closure property with the help of numerical as well as algebraic expressions.

The closure property if we define an multiplication operation is given by:

With the help of numerical expression.

Let us consider

and  

Then

and

Hence

Hence, the closure property holds.

similar case holds for algebraic expression as well.

Since we know that:

Similarly rational expression holds closure property with respect to addition as well.

i.e. a+b=b+a

But it does not hold in case of subtraction.

( since a-b≠b-a

consider a=3 and b= 5

Then a-b=3-5= -2

and b-a=5-3=2 )

Step-by-step explanation:

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