Question

( frac{x^{4}}{(x-1)(x+2)}=frac{x^{4}}{x^{2}+x-2} )
( x^{2}+x-2 int frac{x^{2}-x+3}{x^{4}} )
( x^{4}+x^{3}-2 x^{2} )
( -x^{3}+2 x^{2} )
( -x^{3}+x^{2}+2= )
( 3 x^{2}+ )
( -frac{--}{5 x+6} )
( operatorname{fic} frac{x^{4}}{(x-1)(x+2)}=frac{left(x^{2}+x-2right)left(x^{2}-x+3right)+6}{(x-1)(x+2)} )
( frac{x^{4}}{(x-1)(x+2)}=x^{2}-x+3+frac{6-5 x}{(x-1)(x+2)}-2 )
Solwing thesc ( 2 e q^{n} s rightarrow A=1 / 3 quad & cdot b=frac{-16}{3} )
( frac{x^{4}}{(x-1)(x+2)}=x^{2}-x+3+frac{1}{3(x-1)}=frac{16}{13(x+2)} )
on coniparing this eq. Kwith the given ( =3 )
the

# 16 (x-1)(x+2) ---+ x2x+k, then k = 3(x-1) 3(x+2) (b) 1 (c) 2 (a) o (d) 3

Solution