# Algebra Examples

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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.

Simplify by cancelling.

Cancel the common factor of .

Write as a fraction with denominator .

Factor out the greatest common factor .

Cancel the common factor.

Rewrite the expression.

Simplify.

Multiply and .

Divide by .

Simplify the numerator.

Remove parentheses around .

Raise to the power of .

Multiply by .

Raise to the power of .

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

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

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.

Write as a fraction with denominator .

Factor out the greatest common factor .

Cancel the common factor.

Rewrite the expression.

Simplify.

Multiply and .

Divide by .

Add and .

Subtract from .

Simplify the denominator.

Multiply by .

Multiply by .

Multiply by .

Add and .

Divide by .