%2F(x%2B3).jpeg "(x^2+7x+12)/(x+3)")
Simplifying the Rational Expression (x^2+7x+12)/(x+3)
This article will guide you through simplifying the rational expression (x^2+7x+12)/(x+3).
Understanding Rational Expressions
A rational expression is simply a fraction where the numerator and denominator are polynomials. In our case, we have:
- Numerator: x^2 + 7x + 12
- Denominator: x + 3
Simplifying the Expression
The key to simplifying this expression is factoring. Let's break it down:
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Factor the numerator: x^2 + 7x + 12 can be factored into (x+3)(x+4)
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Rewrite the expression: Now our expression becomes: [(x+3)(x+4)] / (x+3)
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Cancel common factors: Notice that (x+3) appears in both the numerator and denominator. We can cancel these out, leaving us with: (x+4)
Result
Therefore, the simplified form of the rational expression (x^2+7x+12)/(x+3) is (x+4).
Important Note
It is crucial to remember that this simplification is valid only when x ≠ -3. This is because when x = -3, the original expression becomes undefined (division by zero).