24^2-10x-21/32x^2-81

To simplify the given expression, we can follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders, Multiplication/Division, and Addition/Subtraction. Let's break down the problem step by step:

Step 1: Simplify the numerator.
The numerator is (24^2 - 10x - 21).

To start, we can simplify the square of 24, which is 576. So now we have (576 - 10x - 21).

Step 2: Simplify the denominator.
The denominator is (32x^2 - 81).

We can observe that both terms in the denominator are perfect squares. The first term, 32x^2, can be rewritten as (4x)^2. The second term, 81, is a perfect square itself.

Now, applying the formula (a^2 - b^2) = (a + b)(a - b) to the denominator, we have:
(32x^2 - 81) = ((4x)^2 - 9^2) = ((4x + 9)(4x - 9)).

Step 3: Simplify the fraction.
We are left with (576 - 10x - 21) / ((4x + 9)(4x - 9)).

At this point, we have simplified the given expression as much as possible. The expression cannot be further reduced without additional information or specific values for x.

So, the simplified form of the expression (24^2 - 10x - 21) / (32x^2 - 81) is (576 - 10x - 21) / ((4x + 9)(4x - 9)).