Final answer:
The algebraic operation involves simplification, multiplication, and division of algebraic expressions. It is simplified by combining like terms and reducing common factors. The exact simplest form depends on whether additional common factors exist between the numerator and denominator.
Step-by-step explanation:
The student is asking how to perform an algebraic operation and express the result in its simplest form. The specific operation in question involves multiplying a fraction by another expression and then dividing the result by a third expression. This type of problem involves skills such as simplification, multiplication, and division of algebraic expressions, which are typically covered in high school algebra courses.
To simplify the given expression (23 / 1) × (x² - 72 - 8) / (x² - 24), one approach is to combine like terms in the numerator and reduce any common factors between the numerator and the denominator. The expression simplifies to 23 × (x² - 80) / (x² - 24). Assuming there are no further simplifications (e.g., a factorable quadratic), this might be the simplest form. However, if the denominator factors into something like (x + a)(x - b) and one of these binomials is a factor of the numerator, further simplification would be necessary. Without specific values for x or additional context from the question, we can’t provide a more exact answer. But in general, working with algebraic expressions like this is about finding ways to reduce and rewrite the expressions until they are in their most minimal form.