Problem 31
Question
Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{3 x+9}{x+3}$$
Step-by-Step Solution
Verified Answer
The simplified form of the rational expression \(\frac{3 x+9}{x+3}\) is 3.
1Step 1: Recognize the Rational Expression
A rational expression is a fraction where both the numerator and denominator are polynomials. In this exercise, the given rational expression is \(\frac{3x+9}{x+3}\). This expression can be factored to find common factors.
2Step 2: Factor out the Common Factors
Next, look for common factors in the numerator and the denominator. In the given expression, the numerator \(3x+9\) can be factored as \(3(x+3)\). The denominator is \(x+3\). The term \(x+3\) appears both in the numerator and denominator.
3Step 3: Cancel out the Common Factors
Common factors in the numerator and denominator of a rational expression can be canceled out. In our expression, both \(x+3\) in the numerator and denominator cancel each other out. Thus, the simplified form of the rational expression is 3.
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