# Finite Math Examples

Find the Domain of the Quotient
,
Distribute the value across the operation.
Evaluate .
Replace the variable with in the expression.
Simplify the result.
Multiply by to get .
Evaluate .
Replace the variable with in the expression.
Simplify the result.
Multiply by to get .
Compose the result function for by replacing the function designators with the actual functions.
Rewrite the division as a fraction.
Solve to find the value of that makes the expression undefined.
Set up the equation to solve for .
Since does not contain the variable to solve for, move it to the right side of the equation by subtracting from both sides.
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 to get .
For asymptotes and point discontinuity (denominator equals ), it is easier to find where the expression is undefined. These values are not part of the domain.
The domain is all values of that make the expression defined.

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