Algebraic Constraint Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
What values does 1xโˆ’3\frac{1}{x-3} constrain xx to avoid?

Solution

  1. 1
    Step 1: The denominator xโˆ’3x - 3 cannot be zero.
  2. 2
    Step 2: xโˆ’3โ‰ 0x - 3 \neq 0, so xโ‰ 3x \neq 3.
  3. 3
    Step 3: The domain is all real numbers except x=3x = 3.

Answer

xโ‰ 3x \neq 3
Division by zero is undefined, creating a constraint on the domain. Rational expressions implicitly carry constraints that exclude values making any denominator zero.

About Algebraic Constraint

A mathematical condition expressed as an equation or inequality that restricts which values the variables are allowed to take.

Learn more about Algebraic Constraint โ†’

More Algebraic Constraint Examples

Example 1 easy

What constraint does [formula] impose on [formula]?

Example 3 easy

What constraint does [formula] impose on [formula]?

Example 4 medium

If [formula] and [formula], what is the maximum of [formula]?

โ† All Algebraic Constraint Examples Algebraic Constraint Concept