1) \(\frac{x+1}{2x-2}+\frac{x^2+3}{2-2x^2}\)
\(=\frac{-4x^2+8x-4}{-4x^3+4x^2+4x-4}\)
\(=\frac{-x^2+2x-1}{-x^3+x^2+x-1}\)
\(=\frac{\left(-x+1\right)\left(x-1\right)}{\left(-x-1\right)\left(x-1\right)\left(x-1\right)}\)
\(=\frac{1}{x+1}\)
2) \(\frac{1-2x}{2x}+\frac{2x}{2x-1}+\frac{1}{2x-4x^2}\)
\(=\frac{-16x^3+16x^2-4x}{-16x^4+16x^3-4x^2}\)
\(=\frac{-16x^2+16x-4}{-16x^3+16x^2-4x}\)
\(=\frac{-4x^2+4x-1}{-4x^3+4x^2-x}\)
\(=\frac{\left(-2x+1\right)\left(2x-1\right)}{x\left(-2x+1\right)\left(2x-1\right)}\)
\(=\frac{1}{x}\)
