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Chapter 7: Problem 28

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

Short Answer

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

Step by step solution

01

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 \(\frac{12}{6(x - 3)}\)
02

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 \(\frac{2}{x - 3}\)
03

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.

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Most popular questions from this chapter

perform the indicated operations. Simplify the result, if possible. $$\left(\frac{3 x-1}{x^{2}+5 x-6}-\frac{2 x-7}{x^{2}+5 x-6}\right) \div \frac{x+2}{x^{2}-1}$$

Will help you prepare for the material covered in the next section. If \(B=k W,\) find the value of \(k,\) in decimal form, using \(B=5\) and \(W=160\)

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