Problem 28 - Introductory Algebra for College Students

Question

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{12}{6 x-18}$$

Step-by-Step Solution

Answer

The simplified form of the expression \(\frac{12}{6x - 18}\) is \(\frac{2}{x - 3}\)

Step 1: Factor out the Greatest Common Factor from the numerator and denominator

In this case, the greatest common factor in the denominator (6x - 18) is 6. We can factor out 6 from the expression to get \(6( x - 3)\). The numerator is just 12. Thus, our expression becomes \(\frac{12}{6(x - 3)}\)

Step 2: Simplify the Expression

After factoring out the common factor, we can simplify the fraction by canceling out any common factors. In this case, the number 6 in the numerator and the denominator. After this simplification, we get \(\frac{2}{x - 3}\)

Step 3: Check Your Result

After simplifying the expression, always review the result to ensure that it cannot be simplified further. In this case, \(\frac{2}{x - 3}\) is the simplest form of the original expression and cannot be simplified further.