## Simplifying the Rational Expression: (x^2 + 5x + 6) / (x + 2)

This article will guide you through the process of simplifying the rational expression (x^2 + 5x + 6) / (x + 2).

### Understanding Rational Expressions

A rational expression is a fraction where the numerator and denominator are polynomials. Simplifying a rational expression means finding an equivalent expression with a simpler form.

### Factoring the Numerator

The first step in simplifying this expression is to factor the numerator. The quadratic expression (x^2 + 5x + 6) can be factored into (x + 2)(x + 3).

### Simplifying the Expression

Now, our expression looks like this:

(x + 2)(x + 3) / (x + 2)

Notice that both the numerator and denominator share a common factor of (x + 2). We can cancel out this common factor, leaving us with:

**x + 3**

### Restrictions

It's important to note that simplifying the expression does not change its value for all possible values of *x*. The original expression is undefined when *x* = -2, as this would result in division by zero. Therefore, the simplified expression *x* + 3 is also undefined when *x* = -2.

### Conclusion

By factoring and canceling common factors, we have successfully simplified the rational expression (x^2 + 5x + 6) / (x + 2) to **x + 3**, with the restriction that *x* cannot equal -2.