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

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( 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

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