Problem 1 - 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. $$\frac{5}{2 x}$$

Step-by-Step Solution

Answer

The rational expression is undefined when \(x = 0\).

Step 1: Identify the Denominator

In the rational expression \(\frac{5}{2x}\), the denominator is \(2x\). So, we should find out for what value of \(x\) the denominator equals zero, because division by zero is undefined in mathematics.

Step 2: Set Denominator Equal to Zero and Solve

Equation to solve for is \(2x = 0\). Solving this equation, we get \(x = 0\).

Step 3: Identify the Undefined Number

Now that we've found that \(x = 0\) makes the denominator equal to zero, we can conclude that the rational expression \(\frac{5}{2x}\) is undefined when \(x = 0\).