Which solution to the equation 1/x-1=x-2/2x^2-2 is extraneous?

An extraneous solution is a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the original problem.

Given the equation:


From the equation, it is obtained that x = 1 and x = -4 are the solutions of the equation.

Now, we substitute x = 1 into the equation as follows:


As can be see, for x = 1, the equation is undefined.

Now, we substitute x = -4 into the equation as follows:


It can be seen that x = -4 is a valid solution of the orignal equation.

Therefore, x = 1 is an extraneous solution to the equation