2x-2/x^2-2x+1=x+2/x^2+4x+4 is unsolvable?

2x - 2/x² - 2x + 1   =   x + 2/x² + 4x + 4

Simplifying the left side:  2x - 2x  = 0.

Simplifying the right side:  x + 4x  =  5x

- 2/x² + 1  =  2/x² + 5x + 4

Further simplifying:

             0  =  4/x² + 5x + 3

Multiplying both sides by x²:     0  =  4 + 5x³ + 3x²

This will have a solution, you can approximate it by graphing:  y  =  5x³ + 3x² + 4.

[And, like the quadratic equation, there is a cubic equation, but it's not simple.]