Option C: [tex]\frac{x^{2}-9}{x^{2}-4}[/tex] is the product of the rational expression.
Explanation:
The given rational expression is [tex]\frac{x+3}{x+2} \cdot \frac{x-3}{x-2}[/tex]
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;
[tex]\frac{(x+3)(x-3)}{(x+2)(x-2)}[/tex]
Let us use the identity [tex](a+b)(a-b)=a^2-b^2[/tex] in the above expression.
Thus, we get;
[tex]\frac{x^{2} -3^2}{x^{2} -2^2}[/tex]
Simplifying the terms, we get;
[tex]\frac{x^{2}-9}{x^{2}-4}[/tex]
Thus, the product of the rational expression is [tex]\frac{x^{2}-9}{x^{2}-4}[/tex]
Hence, Option C is the correct answer.
