# Algebra Examples

,

Step 1

Write as an equation.

Step 2

Step 2.1

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.

Step 2.2

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

Step 3

Step 3.1

Multiply the numerator and denominator of the fraction by .

Step 3.1.1

Multiply by .

Step 3.1.2

Combine.

Step 3.2

Apply the distributive property.

Step 3.3

Cancel the common factor of .

Step 3.3.1

Cancel the common factor.

Step 3.3.2

Rewrite the expression.

Step 3.4

Simplify the numerator.

Step 3.4.1

Raise to the power of .

Step 3.4.2

Multiply by .

Step 3.4.3

Raise to the power of .

Step 3.4.4

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

Step 3.4.5

Combine and .

Step 3.4.6

Combine the numerators over the common denominator.

Step 3.4.7

Simplify the numerator.

Step 3.4.7.1

Multiply by .

Step 3.4.7.2

Add and .

Step 3.4.8

Cancel the common factor of .

Step 3.4.8.1

Move the leading negative in into the numerator.

Step 3.4.8.2

Cancel the common factor.

Step 3.4.8.3

Rewrite the expression.

Step 3.4.9

Add and .

Step 3.4.10

Subtract from .

Step 3.5

Simplify the denominator.

Step 3.5.1

Multiply by .

Step 3.5.2

Multiply .

Step 3.5.2.1

Multiply by .

Step 3.5.2.2

Multiply by .

Step 3.5.3

Add and .

Step 3.6

Divide by .