Final answer:
To simplify the expression (x² + 6x + 8) / (x + 2), the numerator is factored to (x + 2)(x + 4). The common factor (x + 2) is canceled out, leaving the simplified expression x + 4.
Step-by-step explanation:
To simplify the expression quantity x squared plus 6 x plus 8 end quantity over quantity x plus 2, we need to factor the numerator, if possible, and see if it has any common factors with the denominator that can be canceled out. This is a technique often used to simplify rational expressions.
The factored form of x² + 6x + 8 is (x + 2)(x + 4), because when you multiply these two binomials using FOIL (First, Outer, Inner, Last), you get the original quadratic expression. Now, you can see that the (x + 2) terms in the numerator and denominator can be canceled out, assuming x is not equal to -2 (since division by zero is undefined).
After canceling, the simplified form of the expression is just x + 4.
In summary, the simplified expression is:
(x² + 6x + 8) / (x + 2) = (x + 4)