Which solution to the equation (1/x-1)=(x-2/2x^2 -2) is extraneous? a. x=1 and x=-4 b. nether x=1 or x=-4 c. x=1 d. x=-4

Any "solution" that makes a denominator zero will be extraneous.

The appropriate choice is ...
  c. x=1


This can be solved without extraneous solutions by subtracting the right side.
  (2(x +1) -(x -2))/(2(x -1)(x +1)) = 0
  (x +4) = 0 . . . . . . . . . . . . . . . . . . . . . multiply by the denominator
  x = -4 . . . . . . . . . . . . . . . . . . . . . . . . subtract 4