is equal to :

Correct option is D

Step 1: Factorize the Numerator and Denominator.
Numerator: 15(x² - 2x - 15)
The quadratic expression x² - 2x - 15 can be factored as:
x² - 2x - 15 = (x - 5)(x + 3)
So, the numerator becomes: 15(x - 5)(x + 3).
Denominator: 25(x + 3)(x² - 25)
Notice that x² - 25 is a difference of squares:
x² - 25 = (x - 5)(x + 5)
So, the denominator becomes: 25(x + 3)(x - 5)(x + 5).
Step 2: Rewrite the Expression with Factored Terms:
Expression: [15(x - 5)(x + 3)] / [25(x + 3)(x - 5)(x + 5)].
Step 3: Cancel Common Factors:
The terms (x - 5) and (x + 3) are present in both the numerator and the denominator, so they can be canceled:
Result: [15 / 25(x + 5)].
Step 4: Simplify the Coefficient:
15/25 = 3/5
So, the simplified expression becomes: 3 / [5(x + 5)].