Consider the difference quotient formula.

Evaluate the function at .

Replace the variable with in the expression.

The final answer is .

Find the components of the definition.

Plug in the components.

Simplify the numerator.

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

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 .

Multiply and .

Multiply and .

Reorder the factors of .

Combine the numerators over the common denominator.

Rewrite in a factored form.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Simplify.

Add and .

Apply the distributive property.

Subtract from .

Subtract from .

Factor out negative.

Combine exponents.

Factor out negative.

Multiply by .

Rewrite.

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Since both terms are perfect squares, factor using the difference of squares formula, where and .

Simplify.

Add and .

Apply the distributive property.

Subtract from .

Subtract from .

Factor out negative.

Combine exponents.

Factor out negative.

Multiply by .

Remove unnecessary parentheses.

Move the negative in front of the fraction.

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of .

Move the leading negative in into the numerator.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move the negative in front of the fraction.

Find the Difference Quotient f(x)=8/(x^2)