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Chapter 7: Problem 29

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{-15}{3 x-9}$$

Short Answer

Expert verified
The simplified form of the provided rational expression is \( \frac{-5} {x-3} \)

Step by step solution

01

Factor Out Common Factors

Both -15 and 9 are divisible by 3, and the denominator also has a variable x. So, the first step is to factor the numbers and variables in both the numerator and the denominator. As a result, the expression becomes \( \frac{-3 \times 5} {3 \times (x-3)} \)
02

Cancel Out Common Factors

The next step is to cancel out the common factors from the numerator and the denominator. Here, 3 is common in both, and thus can be cancelled out. The resulting expression is \( \frac{-5} {x-3} \)
03

Simplification

The previous step produced the simplified version of the rational expression, so no further simplification is possible.

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Most popular questions from this chapter

Explain how to add rational expressions when denominators are opposites. Use an example to support your explanation.

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. $$\frac{x^{2}-13}{x+4}-\frac{3}{x+4}=x+4, x \neq-4$$

perform the indicated operation or operations. Simplify the result, if possible. $$\frac{22 b+15}{12 b^{2}+52 b-9}+\frac{30 b-20}{12 b^{2}+52 b-9}-\frac{4-2 b}{12 b^{2}+52 b-9}$$

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?

Add or subtract as indicated. Simplify the result, if possible. $$\frac{3}{x}+\frac{4}{x-6}$$
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