Question

Find the coefficient of :
$x^n$ in the expansion of $\frac{3x^2-2}{x+x^2}$

Answer 1

$y=\frac{3x}{1+x}-\frac{2}{x+x^2}$

$=3x(1+x{)}^{-1}-\frac{2}{x}(1+x{)}^{-1}$

coefficient of $x^n$=3.coefficient of $x^{n-1}$ -2.coefficient of $x^{n+1}$ in expansion of $(1+x{)}^{-1}$

$=3.(-1{)}^{n-1}-2.(-1{)}^{n+1}$

we know the expansion

$(1+x{)}^{-1}=1-x+x^2........$