1. Find the solution set
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Answer:
given ∣x+
x
1
∣>2
⇒∣
x
x
2
+1
∣>2
∣x∣
∣x
2
+1∣
=
∣x∣
x
2
+1
>2
⇒x
2
+1>2∣x∣
⇒x
2
−2∣x∣+1>0
if x>0 then (x−1)
2
>0 it is possible for all x
therefore the solution is x>0
if x<0 then (x+1)
2
>0 it is also possible for all x
therefore the solution set is x<0
therefore the overall solution set is x∈R−1
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