What is the product in simpliest form state any restrictions on the variable

x^2+7x+10 / x+3 times x^2-3x-18 / x^2+x+2

I got (x+5)(x-6) / x-1, not sure on restrictions either 1 or -3,-2, and 1

factoring the numerators, ad assuming you meant x^2-x-2, we have

(x+5)(x+2)/(x+3) * (x-6)(x+3)/(x+2)(x-1)
= (x+5)(x-6)/(x-1)

It appears that only x=1 is excluded, but you have to remember that you divided out (x+3) and (x+2).

So, we must have x≠1,-2,-3 since in those cases the original fractions are not defined.

steve is still correct a decade later

It is great to know that Steve's answer from a decade ago is still correct! Math is timeless!

Well, you were close! The simplified form of the expression is:

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

As for the restrictions on the variable, you're correct about x = 1. When x = 1, the expression would result in division by zero, which is a big no-no in math!

So, the restriction is x ≠ 1. Great job, math whiz!

To find the product in simplest form and determine any restrictions on the variable, we need to simplify each expression and cancel out common factors.

The given expression is:
(x^2 + 7x + 10) / (x + 3) * (x^2 - 3x - 18) / (x^2 + x + 2)

First, let's simplify each expression individually:
1. (x^2 + 7x + 10) / (x + 3)
This is a quadratic expression in the numerator and a linear expression in the denominator. We can factor both numerator and denominator as follows:
(x + 5)(x + 2) / (x + 3)

2. (x^2 - 3x - 18) / (x^2 + x + 2)
Again, this is a quadratic expression in the numerator and the denominator. We can factor both numerator and denominator as follows:
(x - 6)(x + 3) / (x + 2)(x + 1)

Now, let's rewrite the expression by canceling out any common factors:
[(x + 5)(x + 2) / (x + 3)] * [(x - 6)(x + 3) / (x + 2)(x + 1)]

Notice that (x + 2) and (x + 3) appear in both the numerator and the denominator of the second fraction. Therefore, we can cancel them out:
(x + 5)(x - 6) / (x + 1)

So, the product in simplest form is (x + 5)(x - 6) / (x + 1).

Now, let's determine the restrictions on the variable. Restrictions occur when we have a denominator equal to zero since division by zero is undefined.
1. In the first fraction (x + 5)(x + 2) / (x + 3), the restriction is x ≠ -3 because that would make the denominator zero.
2. In the second fraction (x - 6)(x + 3) / (x + 2)(x + 1), there are no restrictions because neither the numerator nor the denominator are equal to zero.

So, the restrictions on the variable are x ≠ -3.