SOLUTION: how can i decompose this partial fraction(4x^3)/(x^3-x^2)

Algebra ->  Matrices-and-determiminant -> SOLUTION: how can i decompose this partial fraction(4x^3)/(x^3-x^2)       Log On


   

Question 745514: how can i decompose this partial fraction(4x^3)/(x^3-x^2)
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
This is not a "proper" decomposition problem. Typically the degree of the denominator is greater than the degree of the numerator...
but...we can still simplify...
notice that this expression can be factored:
%284x%5E3%29%2F%28x%5E3-x%5E2%29=%28%28x%5E2%29%284x%29%29%2F%28%28x%5E2%29%28x-1%29%29
from here we notice that by polynomial long division (don't know how to show using this editor) that:
x%2F%28x-1%29=1%2B1%2F%28x-1%29
so our expression simplifies to...

%284%2B4%2F%28x-1%29%29

:)