Question

Consider the product: x² - 3x - 10/x² - 6x + 5·x - 2/x - 5. What is the simplest form of this product? The numerator is _______ and the denominator is _______. The expression has an excluded value of x = _______.

Answer 1

To find the simplest form of the expression, factorize the numerator and denominator separately, then combine them. The excluded value of x is 5.

Step-by-step explanation:

To find the simplest form of the given expression, we need to simplify the numerator and denominator separately and then combine them. Let's start with the numerator:

Factorizing x² - 3x - 10, we get (x - 5)(x + 2).

Now, let's simplify the denominator:

Factorizing x² - 6x + 5·x - 2, we get (x - 1)(x - 5).

Combining the numerator and denominator, the simplest form becomes (x - 5)(x + 2) / (x - 1)(x - 5).

However, the expression has an excluded value of x = 5 since it causes a zero in both the numerator and denominator. Hence, the numerator is (x - 5)(x + 2), the denominator is (x - 1)(x - 5), and the expression has an excluded value of x = 5.