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

Jul 8, 2015

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

#### Explanation:

$\frac{{x}^{3} + 1}{{x}^{3} - {x}^{2} + x} . \frac{3 x}{- 12 x - 12}$

if you see carefully we can take out -12 common from (12x-12) term, x from $\left({x}^{3} - {x}^{2} + x\right)$
doing so

$\frac{{x}^{3} + 1}{\left(x\right) \left({x}^{2} - x + 1\right)} . \frac{3 x}{\left(- 12\right) . \left(x + 1\right)}$

now cancelling x and dividing 12 with 3 we get

$\frac{{x}^{3} + 1}{{x}^{2} - x + 1} . \frac{1}{\left(- 4\right) . \left(x + 1\right)}$

multiplying $\left({x}^{2} - x + 1\right)$ and $\left(x + 1\right)$
we get

$\frac{{x}^{3} + 1}{{x}^{3} - {x}^{2} + x + {x}^{2} - x + 1} . \frac{1}{\left(- 4\right)}$

now cancelling the common terms in denominator we get

$\frac{{x}^{3} + 1}{{x}^{3} + 1} . \frac{1}{\left(- 4\right)}$

now cancelling common terms in numerator and denominator

we get the final answer to be

$\frac{1}{\left(- 4\right)}$ or $\frac{- 1}{4}$