Expand x/(1+X)(1-3X) in ascending power of x order 3
the way you typed it ...
= x(1-3x)/(x+1)
= x( -3 + 4/(x+1) )
look at the 4/(x+1) , by long algebraic division we get
4/(x+1) = 4 - 4x + 4x^2 - 4x^3 + ...
using 4(1+x)^-1 and expanding it by the Binomial Theorem gives the same result
so x( -3 + 4/(x+1) )
= x( -3 + (4 - 4x + 4x^2 - 4x^3 + ...) )
= x - 4x^2 - 4x^3 + ..
check my algebra