Problem 23 - Introductory Algebra for College Students

Question

Simplify each rational expression. If the rational expression cannot be simplified, so state. $$\frac{5 x-15}{25}$$

Step-by-Step Solution

Answer

\(\frac{x-3}{5}\)

Step 1: Factorize the numerator and denominator

In the example provided, \(5x-15\) is the numerator and \(25\) is the denominator. We can factorize the numerator as \(5(x-3)\). The denominator \(25\) is a prime number, so it can't be factorized further. Thus, the factored form of the rational expression is \(\frac{5(x-3)}{25}\).

Step 2: Simplify the rational expression

Now, we look for the common factors in the numerator and the denominator. We can see that both contain \(5\) as a common factor. We divide both the numerator and the denominator by this common factor to get the simplified rational expression: \(\frac{x-3}{5}\).