Question

Which of the following is the product of the rational expression shown below

Answer 1

Option C:
`(x^(2)-9)/(x^(2)-4)` is the product of the rational expression.

Step-by-step explanation:

The given rational expression is
`(x+3)/(x+2) \cdot (x-3)/(x-2)`

We need to determine the product of the rational expression.

Product of the rational expression:

Let us multiply the rational expression to determine the product of the rational expression.

Thus, we have;

`((x+3)(x-3))/((x+2)(x-2))`

Let us use the identity
`(a+b)(a-b)=a^2-b^2` in the above expression.

Thus, we get;

`(x^(2) -3^2)/(x^(2) -2^2)`

Simplifying the terms, we get;

`(x^(2)-9)/(x^(2)-4)`

Thus, the product of the rational expression is
`(x^(2)-9)/(x^(2)-4)`

Hence, Option C is the correct answer.