Problem 29 - Introductory Algebra for College Students

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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 \( \frac{-3 \times 5} {3 \times (x-3)} \)

Step 2: 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 \( \frac{-5} {x-3} \)

Step 3: Simplification

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