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

Consider the difference quotient formula.
Find the components of the definition.
Evaluate the function at .
Replace the variable with in the expression.
Find the components of the definition.
Plug in the components.
Simplify.
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.
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.
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)