Question
X squared plus 5x + 6 / x + 2
Answers
Answered by
GPT-4o mini
To simplify the expression \(\frac{x^2 + 5x + 6}{x + 2}\), we can first factor 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 \(x\)). The numbers \(2\) and \(3\) work because \(2 \times 3 = 6\) and \(2 + 3 = 5\).
This allows us to factor the numerator:
\[
x^2 + 5x + 6 = (x + 2)(x + 3)
\]
Now we can rewrite the original expression using this factorization:
\[
\frac{x^2 + 5x + 6}{x + 2} = \frac{(x + 2)(x + 3)}{x + 2}
\]
As long as \(x + 2 \neq 0\) (or \(x \neq -2\)), we can cancel \(x + 2\) from the numerator and the denominator:
\[
= x + 3 \quad \text{for } x \neq -2
\]
So the simplified form of the expression \(\frac{x^2 + 5x + 6}{x + 2}\) is:
\[
x + 3 \quad (x \neq -2)
\]
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 \(x\)). The numbers \(2\) and \(3\) work because \(2 \times 3 = 6\) and \(2 + 3 = 5\).
This allows us to factor the numerator:
\[
x^2 + 5x + 6 = (x + 2)(x + 3)
\]
Now we can rewrite the original expression using this factorization:
\[
\frac{x^2 + 5x + 6}{x + 2} = \frac{(x + 2)(x + 3)}{x + 2}
\]
As long as \(x + 2 \neq 0\) (or \(x \neq -2\)), we can cancel \(x + 2\) from the numerator and the denominator:
\[
= x + 3 \quad \text{for } x \neq -2
\]
So the simplified form of the expression \(\frac{x^2 + 5x + 6}{x + 2}\) is:
\[
x + 3 \quad (x \neq -2)
\]