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The equation |x|+|x/(x-1)|=x^(2)/(|x-1|)...

The equation `|x|+|x/(x-1)|=x^(2)/(|x-1|)` is always true for x belongs to A) {0} , B) `(1, infty)`, C) `(-1,1)`, D) `(-infty,infty)`

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`x^(2)/|x-1|=|x+x/(x-1)|`
`therefore |x|+|x/(x-1)|=|x+x/(x-1)|` is true only if `(x.x/(x-1)) ge0 rArr x in {0} cup (1,infty)`. Ans. (A)
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