# Simplify (a^2-4a-21)/(a^(2-6)a+8)*(a-4)/(a^2-2a-35)

Factor using the AC method.
Consider the form . Find a pair of integers whose product is and whose sum is . In this case, whose product is and whose sum is .
Write the factored form using these integers.
Simplify the denominator.
Multiply by by adding the exponents.
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.
Subtract from .
Rewrite as .
Rewrite as .
Since both terms are perfect cubes, factor using the sum of cubes formula, where and .
Simplify.
Rewrite the expression using the negative exponent rule .
To write as a fraction with a common denominator, multiply by .
Combine the numerators over the common denominator.
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Multiply by .
Rewrite the expression using the negative exponent rule .
Rewrite the expression using the negative exponent rule .
Multiply .
Multiply by .
Combine and .
Move the negative in front of the fraction.
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 .
Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Combine the numerators over the common denominator.
To write as a fraction with a common denominator, multiply by .
Combine the numerators over the common denominator.
Multiply and .
Multiply by by adding the exponents.
Multiply by .
Raise to the power of .
Use the power rule to combine exponents.