1/x+2=2/x-1 identify all values of X that make the equation true

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  as written: x = 1/3

  as maybe intended: x =  -5

Step-by-step explanation:

As written

  (1/x) +2 = (2/x) -1

  3 = 1/x . . . . . . . . . add 1-(1/x)

  x = 1/3

__

As maybe intended

  1/(x +2) = 2/(x -1)

  x -1 = 2(x +2) . . . . . . . multiply by (x+2)(x-1)

  x -1 = 2x +4 . . . . . . . . eliminate parentheses

  -5 = x . . . . . . . . . . . . . subtract (x+4)