Problem 1 - College Algebra

Question

Find all numbers that must be excluded from the domain of each rational expression. $$\frac{7}{x-3}$$

Step-by-Step Solution

Answer

So, the number 3 should be excluded from the domain of given rational expression because it makes the denominator equals to zero.

Step 1: Understand the Rational Expression

A rational expression is undefined when its denominator equals to zero. So, the purpose of this problem is to find the values of x that will make the rational expression \(\frac{7}{x - 3}\) undefined, meaning the denominator equals to zero.

Step 2: Set the Denominator Equal to Zero

To find when the expression is undefined, set the denominator equal to zero and solve for x. So, \(x - 3 = 0\)

Step 3: Solve for x

By adding 3 to both sides of the equation: \(x = 3\)