What is the product in simplest form? State any restrictions on the variable. x^2 + 5x + 6/x + 4 times x^2 + x - 12/ x^2 + x - 2
To find the product, we need to multiply the two expressions together:
(x^2 + 5x + 6)/(x + 4) * (x^2 + x - 12)/(x^2 + x - 2)
Next, we can simplify each expression individually.
The first expression (x^2 + 5x + 6)/(x + 4) can be factored as (x + 2)(x + 3)/(x + 4).
The second expression (x^2 + x - 12)/(x^2 + x - 2) can be factored as (x - 3)(x + 4)/(x - 1)(x + 2).
Now, we can cancel out common factors in the numerator and denominator:
[(x + 2)(x + 3)/(x + 4)] * [(x - 3)(x + 4)/(x - 1)(x + 2)]
After canceling out common factors, we're left with:
(x + 3)/(x - 1)
So, the product in simplest form is (x + 3)/(x - 1).
Restriction:
The variable x cannot be equal to 1, as it would lead to division by zero in the final expression.