# Precalculus Examples

Find the Difference Quotient
Consider the difference quotient formula.
Find the components of the definition.
Evaluate the function at .
Replace the variable with in the expression.
Simplify the result.
Rewrite as .
Expand using the FOIL Method.
Apply the distributive property.
Apply the distributive property.
Apply the distributive property.
Simplify and combine like terms.
Simplify each term.
Multiply by .
Multiply by .
Add and .
Reorder and .
Add and .
Apply the distributive property.
Multiply by .
The final answer is .
Find the components of the definition.
Plug in the components.
Simplify.
Simplify the numerator.
Multiply by .
Subtract from .
Add and .
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Simplify terms.
Reduce the expression by cancelling the common factors.
Cancel the common factor.
Divide by .
Apply the distributive property.
Multiply by .
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