Question

Simplify x squared plus 5x + 6 / x + 2 write your answer in standard form

Answer 1

To simplify the expression \(\frac{x^2 + 5x + 6}{x + 2}\), we first factor the numerator:

1. The expression \(x^2 + 5x + 6\) can be factored as:
\[
x^2 + 5x + 6 = (x + 2)(x + 3)
\]

2. Now, substitute this factorization back into the original expression:
\[
\frac{(x + 2)(x + 3)}{x + 2}
\]

3. Next, we can cancel the \(x + 2\) terms in the numerator and denominator (provided \(x \neq -2\)):
\[
= x + 3 \quad \text{(for } x \neq -2\text{)}
\]

Thus, the simplified expression in standard form is:
\[
\boxed{x + 3}
\]

(Note: Remember that this simplification is valid for all \(x\) except \(x = -2\), where the original expression is undefined.)