Problem 1 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The number '3' should be excluded from the domain of the rational expression.

Step 1: Set the denominator equal to zero

Setting the denominator equal to zero: \(x - 3 = 0\)

Step 2: Solve the equation

Solving this equation gives the value of 'x' that makes the denominator zero. We simply add three to both sides of the equation: \(x = 3\).

Step 3: Excluded values from the domain

So, 'x' being equals to 3 will make the denominator of the rational expression to be zero and hence undefined. Therefore, '3' should be excluded from the domain of the given rational expression.