$\text{ The coefficient of }{\mathrm{x}}^{\mathrm{n}}\text{ in }\frac{(1+\mathrm{x}{)}^2}{(1-\mathrm{x}{)}^2}\text{ is }$

$\begin{array}{l}\frac{(1+x{)}^2}{(1-x{)}^2}=(1+x{)}^2(1-x{)}^{-2}\\ =\left(1+2x+x^2\right)\left(1+2x+3x^2+\dots ..+\left(n-1\right)x^{n-2}+\left(n\right)x^{n-1}+\left(n+1\right)x^n ..\right)\end{array}$

$\therefore The coefficient of x^n =\left(n+1\right)+2n+n-1=4n$