How to Simplify an Expression with a Polynomial Divided by a Polynomial?

[sallaboy]

Homework Statement

x^2/(1-x)

Homework Equations

none

The Attempt at a Solution

I know I should use some kind of substitute but ... may t=1-x but what next ?

any help will be helpfull
thanks dimitry

 

[Phrak]

using t=1-x replace x in your integrand with x = 1-t. Also dx is replaced.

Find dt as a function of dx.

 

[sallaboy]

ok ... but can I use the same technic when I have:

x^2/(x+2)

?

 

[rl.bhat]

You can rewrite the problem as

(x^2 - 4 + 4)/(x+2)

= (x^2 - 4 )/(x+2) + 4/(x+2)

Now simplify and find the integration.

 

[sallaboy]

thanks a lot !

 

[gomunkul51]

if the degree of the polynomial in the nominator is equal or higher the the degree of the polynomial in the denominator the you have to do polynomial long division to turn the expression to a whole part plus a rational quotient (a fraction with a polynomial in the nominator of a lesser degree then the polynomial in the denominator).

 

[njama]

Another idea:

u=1-x

du=dx

x=1-u

 

[Mark44]

if the degree of the polynomial in the nominator is equal or higher the the degree of the polynomial in the denominator the you have to do polynomial long division to turn the expression to a whole part plus a rational quotient (a fraction with a polynomial in the nominator of a lesser degree then the polynomial in the denominator).

IMO, this is the simplest approach of those presented here.
x^2/(1 - x) = -x^2/(x -1) = -x - 1 - 1/(x - 1).