Could be wrong but, as I can work out, it goes like this:
1/(2x^2+2)+1/(4x-2)=x+2/(4x^2-1)
1+1/(4x-2)=(2x^2+2)(x+2/(4x^2-1)
2=(4x-2)(2x^2+1)(x+2/(4x^2-1))
8x^2-2=(4x-2)(2x^2+1)(4x^3-x+2)
8x^2-2=8x^3-4x^2+4x(4x^3-x+2)
8x^2-2=32x^6-8x^4+16x^3-16x^5+4x^3-8x^2+16x^4-4x^2+8x
32x^6-16x^5+8x^4+12x^3-20x^2+8x+2=0
Which all together makes
Which can then be solved like any old polynomial, which I cba to do right now
Hope this helps