(i) Solve for x if -- > 1 x +X-2
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(i) Solve for x if -- > 1 x +X-2

JEE/Engineering Exams
Maths
Solution
119
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( frac{left|x^{2}-4right|}{x^{2}+x-2}>1 quad ) wr ( x in(-infty, 2) ) Lit ( x in(2, infty) cup(-a,-2) quad frac{-x^{2}+4}{x^{2}+x-2}-1> ) ( frac{x^{2}+4-x^{2}-x+2}{x^{2}+x-2}> ) ( frac{x^{2}-4}{x^{2}+x-4}-1>0 quad frac{-2 x^{2}-x+6}{x^{2}+x-2}> ) ( frac{x^{2}-4-x^{2}-x+2}{x^{2}+x-2}>frac{2 x^{2}+x-6}{x^{2}+x-2}<0 ) ( frac{(2 x-3)(x+1)}{(x-1)(x+2)}<0 ) ( frac{x-2}{x^{2}+x-2}<0 quad frac{(-2)(t)}{-2}+frac{(t)}{1 / 2} ) ( frac{x-2}{(x-1)(x+2)}<0 ) ( frac{1+1,(-),(t)}{1}, quad Rightarrow mid x in(-infty,-2) cup(1,3 /) ) ( operatorname{ctg}(-infty,-1 )
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