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

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Answer 1 · 2016-09-20T18:27:02

#1/(a-4)#

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

=#1/(a-4)#