Discussion

Explanation:

Let x+1x-32 = a

The given equation becomes: 
a2 – 2a – 8 = 0

⇒ (a - 4)(a + 2) = 0
⇒ a = 4 or -2 (rejected since a has to be positive)

x+1x-32 = 4

Case 1: 
x+1x-3 = 2
⇒ x + 1 = 2x – 6
⇒ x = 7

Case 2: 
x+1x-3 = -2
⇒ x + 1 = -2x + 6
⇒ x = 5/3

∴ x can take 2 possible values i.e., 7 and 5/3.

Hence, 2.

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