# Algebra Examples

Find the Domain of the Quotient
,
Distribute the value across the operation.
Evaluate .
Replace the variable with in the expression.
Simplify the result.
Remove parentheses.
Evaluate .
Replace the variable with in the expression.
Simplify the result.
Multiply by .
Compose the result function for by replacing the function designators with the actual functions.
Simplify.
Rewrite the division as a fraction.
Simplify the numerator.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Set the denominator in equal to to find where the expression is undefined.
Divide each term by and simplify.
Divide each term in by .
Reduce the expression by cancelling the common factors.
Cancel the common factor.
Divide by .
Divide by .
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation: