Answer :

The equation can be re–written as



Adding 1 both the sides, we get,



Subtracting 3 both the sides



Clearly, x≠0, as it will lead equation unmeaningful.


Now, two case arise:


Case1: x+2>0


x>–2


In this case |x+2|=x+2






Considering Numerator,


2x–2>0


x>1


x ϵ (1, ) ….(1)


Case 2: x+2<0


x<–2


In this case, |x+2|=–(x+2)






Considering Numerator,


4x+2>0



ut x<–2


Now, from Denominator, we have–


x ϵ (–∞ , 0) …(2)


(1, ) (from 1 and 2)


We can verify the answers using graph as well.



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