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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.