# Algebra Examples

,

Write as an equation.

The average rate of change of a function can be found by calculating the change in values of the two points divided by the change in values of the two points.

Substitute the equation for and , replacing in the function with the corresponding value.

Multiply the numerator and denominator of the complex fraction by .

Multiply by .

Combine.

Apply the distributive property.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Simplify the numerator.

Raise to the power of .

Multiply by .

Raise to the power of .

To write as a fraction with a common denominator, multiply by .

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Add and .

Cancel the common factor of .

Move the leading negative in into the numerator.

Cancel the common factor.

Rewrite the expression.

Add and .

Subtract from .

Simplify the denominator.

Multiply by .

Multiply by .

Multiply by .

Add and .

Divide by .