Question

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

Answer 1

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