To determine the product of the given rational expressions, let's simplify the expression step-by-step.
The given expression is:
[tex]\[
\frac{x+10}{x+3} \cdot \frac{x-10}{x-3}
\][/tex]
### Step 1: Multiply the numerators
Multiply the numerators together:
[tex]\[
(x+10) \cdot (x-10)
\][/tex]
This results in the difference of squares:
[tex]\[
(x+10)(x-10) = x^2 - 10^2 = x^2 - 100
\][/tex]
### Step 2: Multiply the denominators
Multiply the denominators together:
[tex]\[
(x+3) \cdot (x-3)
\][/tex]
This also results in the difference of squares:
[tex]\[
(x+3)(x-3) = x^2 - 3^2 = x^2 - 9
\][/tex]
### Step 3: Combine the simplified numerator and denominator
Now, we place the simplified numerator and denominator together as one rational expression:
[tex]\[
\frac{x^2 - 100}{x^2 - 9}
\][/tex]
Hence, the product of the given rational expressions is:
[tex]\[
\boxed{\frac{x^2 - 100}{x^2 - 9}}
\][/tex]
Therefore, the correct answer is:
D. [tex]\(\frac{x^2 - 100}{x^2 - 9}\)[/tex]
