How do you multiply a/(a-10)div(a^3+6a^2-40a)/(a^2-100)?

Sep 20, 2016

$\frac{1}{a - 4}$

Explanation:

With Algebraic fractions, no matter what operation you are doing and even if you have an equation, the key is to

factorize factorize factorize!!

a/(a-10)div(a^3+6a^2-40a)/(a^2-100)" " (larr"quadratic trinomial")/(larr"difference of squares")

To divide by a fraction, multiply by the reciprocal.

=a/((a-10))xx ((a+10)(a-10))/(a(a^2+6a-40)

=cancela/(cancel(a-10))xx (cancel(a+10)cancel(a-10))/(cancela(cancel(a+10)(a-4) cancel like factors

=$\frac{1}{a - 4}$