(x-1)(x+2) (a) o 1 16 - + x2-x+k, t...
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(x-1)(x+2) (a) o 1 16 - + x2-x+k, then k = 3(x-1) 3(x+2) (b) 1 (c) 2 (d) 3

JEE/Engineering Exams
Maths
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( x^{4} ) ( (x-1)(x+2)=frac{x^{4}}{x^{2}+x-2} ) ( x^{2}+x-2 frac{x^{2}-x+3}{x^{4}} ) ( frac{x^{4}+x^{3}-2 x^{2}}{-x^{3}+2 x^{2}} ) ( frac{-x^{3}+x^{2}+2 x}{3 x^{2}-2 x} ) ( frac{3 x^{2}+3 x-6}{-5 x+6} ) ( operatorname{se,} f sin n(1) rightarrow frac{x^{4}}{(x-1)(x+2)}=frac{left(x^{2}+x-2right)left(x^{2}-x+3right)+6^{-}}{5 x} ) ( =frac{x^{4}}{(x-1)(x+2)}=x^{2}-x+3+frac{6-5 x}{(x-1)(x+2)}-2 ) et, ( frac{x^{2}-x+3+6-5 x}{(x-1)(x+2)}=x^{2}-x+3+frac{A}{x-1}+frac{B}{(x+2)} ) ( =5-5 x=A(x+2)+B(x-1) ) ( Rightarrow A+B=-5 rightarrow(1) & 2 A-B=6 ) on soluing these 2 eq ( ^{h} rightarrow rightarrow quad A=1 / 3 quad & B=frac{16}{3} ) ( frac{x^{4}}{(x-1)(x+2)}=x^{2}-x+3+frac{1}{3(x-1)}=frac{16}{22(0.71+2)} )
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