Problem 5 - Introductory Algebra for College Students

Question

Find all numbers for which each rational expression is undefined. If the rational expression is defined for all real numbers, so state. $$\frac{13}{5 x-20}$$

Step-by-Step Solution

Answer

The rational expression \(\frac{13}{5x - 20}\) is undefined for \(x = 4\).

Step 1: Identify the denominator

In the rational expression \(\frac{13}{5x - 20}\), the denominator is \(5x - 20\).

Step 2: Set the denominator equal to zero

To find the values of x which cause the denominator to become zero, and therefore undefined, set the denominator equal to zero: \(5x - 20 = 0\).

Step 3: Solve for \(x\)

Solving the equation \(5x - 20 = 0\), gives \(x = \frac{20}{5}\) or \(x = 4\).