Question
Simplify x^2+5x+6/x+2 . Write your answer in standard form.(1 point)
Answers
GPT-4o mini
To simplify the expression \(\frac{x^2 + 5x + 6}{x + 2}\), we can factor the quadratic in the numerator.
The expression \(x^2 + 5x + 6\) can be factored as follows:
\[
x^2 + 5x + 6 = (x + 2)(x + 3)
\]
Now, we can substitute this factorization back into the expression:
\[
\frac{x^2 + 5x + 6}{x + 2} = \frac{(x + 2)(x + 3)}{x + 2}
\]
As long as \(x \neq -2\) (to avoid division by zero), we can simplify:
\[
= x + 3
\]
Thus, the simplified form of \(\frac{x^2 + 5x + 6}{x + 2}\) is
\[
\boxed{x + 3}
\]
in standard form.
The expression \(x^2 + 5x + 6\) can be factored as follows:
\[
x^2 + 5x + 6 = (x + 2)(x + 3)
\]
Now, we can substitute this factorization back into the expression:
\[
\frac{x^2 + 5x + 6}{x + 2} = \frac{(x + 2)(x + 3)}{x + 2}
\]
As long as \(x \neq -2\) (to avoid division by zero), we can simplify:
\[
= x + 3
\]
Thus, the simplified form of \(\frac{x^2 + 5x + 6}{x + 2}\) is
\[
\boxed{x + 3}
\]
in standard form.