Question

Consider this product. The simplest form of this product has a numerator of _____ and a denominator of _____. The expression has an excluded value of _____.

Answer 1

To simplify the given expression, factorize the denominators and cancel out any common factors. The simplest form of the product is (x + 2)/(x - 1). The excluded value is x = 1.

Step-by-step explanation:

To simplify the given expression, we need to factorize the denominators and cancel out any common factors. Let's start with the denominators:

x^2 - 6x + 5 = (x - 1)(x - 5)

x - 5 can be cancelled out with the (x - 5) in the numerator:

(x^2 - 3x - 10)/(x - 1) * (x - 2)/(x - 5)

Now, let's simplify the numerator:

x^2 - 3x - 10 = (x - 5)(x + 2)

(x - 5)(x + 2)/(x - 1)

So, the simplest form of the product is (x + 2)/(x - 1). The numerator is (x + 2) and the denominator is (x - 1). The expression has an excluded value at x = 1, since it would make the denominator equal to zero.