# Precalculus Examples

,

Step 1

Consider the difference quotient formula.

Step 2

Step 2.1

Evaluate the function at .

Step 2.1.1

Replace the variable with in the expression.

Step 2.1.2

Simplify the result.

Step 2.1.2.1

Apply the distributive property.

Step 2.1.2.2

The final answer is .

Step 2.2

Reorder and .

Step 2.3

Find the components of the definition.

Step 3

Plug in the components.

Step 4

Step 4.1

Simplify the numerator.

Step 4.1.1

Apply the distributive property.

Step 4.1.2

Multiply by .

Step 4.1.3

Multiply by .

Step 4.1.4

Subtract from .

Step 4.1.5

Add and .

Step 4.1.6

Add and .

Step 4.1.7

Add and .

Step 4.2

Cancel the common factor of .

Step 4.2.1

Cancel the common factor.

Step 4.2.2

Divide by .

Step 5