How do you multiply #(x^3+1 )/(x^3-x^2+x)*(3x)/(-12x - 12)#?

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Answer 1 · 2015-07-08T14:51:27

use of two things
factorization of the numerator and denominator
cancelling out the common terms

#(x^3+1)/(x^3-x^2+x).(3x)/(-12x-12)#

if you see carefully we can take out -12 common from (12x-12) term, x from #(x^3-x^2+x)#
doing so

#(x^3+1)/((x)(x^2-x+1)).(3x)/((-12).(x+1))#

now cancelling x and dividing 12 with 3 we get

#(x^3+1)/(x^2-x+1).(1)/((-4).(x+1))#

multiplying #(x^2-x+1)# and #(x+1)#
we get

#(x^3+1)/(x^3-x^2+x+x^2-x+1).(1)/((-4))#

now cancelling the common terms in denominator we get

#(x^3+1)/(x^3+1).(1)/((-4))#

now cancelling common terms in numerator and denominator

we get the final answer to be

#(1)/((-4))# or #(-1)/(4)#

please feel free to update the answer if it is wrong

Cheerio!