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Chapter 7: Problem 31

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{3 x+9}{x+3}$$

Short Answer

Expert verified
The simplified form of the rational expression \(\frac{3 x+9}{x+3}\) is 3.

Step by step solution

01

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.
02

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.
03

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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Most popular questions from this chapter

Subtract: \(\frac{13}{15}-\frac{8}{45}\) (Section 1.2, Example 9)

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{x-8}{x^{2}-16}-\frac{x-8}{16-x^{2}}$$

perform the indicated operation. Where possible, reduce the answer to its lowest terms. $$\frac{1}{2}+\frac{2}{3}$$

An experienced carpenter can panel a room 3 times faster than an apprentice can. Working together, they can panel the room in 6 hours. How long would it take each person working alone to do the job?

use the GRAPH or TABLE feature of a graphing utility to determine if the subtraction has been performed correctly. If the answer is wrong, correct it and then verify your correction using the graphing utility. $$\frac{x^{2}-13}{x+4}-\frac{3}{x+4}=x+4, x \neq-4$$
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