Question

Simplify \frac{x^2+5x+6}{x+2}. Write your answer in standard form

Answer 1

To simplify the expression \(\frac{x^2 + 5x + 6}{x + 2}\), we start by factoring the numerator.

The quadratic expression \(x^2 + 5x + 6\) can be factored as follows:

1. We look for two numbers that multiply to \(6\) (the constant term) and add up to \(5\) (the coefficient of \(x\)).
2. The numbers \(2\) and \(3\) satisfy this condition since:
- \(2 \cdot 3 = 6\)
- \(2 + 3 = 5\)

Thus, we can factor the numerator as:

\[
x^2 + 5x + 6 = (x + 2)(x + 3)
\]

Now, we can substitute this back into the expression:

\[
\frac{x^2 + 5x + 6}{x + 2} = \frac{(x + 2)(x + 3)}{x + 2}
\]

Assuming \(x + 2 \neq 0\) (which means \(x \neq -2\)), the \(x + 2\) terms in the numerator and denominator can cancel out:

\[
\frac{(x + 2)(x + 3)}{x + 2} = x + 3
\]

Thus, the simplified expression is:

\[
x + 3
\]

Finally, we write the answer in standard form:

\[
\boxed{x + 3}
\]