1) $\frac{2x+3}{2x-2} - \frac{5}{x^{2}-1} = \frac{2x-3}{2x+2}$

2) $\frac{x-2}{x+2} + \frac{x}{x-2} = \frac{8}{x^{2}-4}$

3) $\frac{3}{2x} = \frac{x+2}{x^{2}-3x}$

4) $\frac{1}{x^{2}-2x+1} = \frac{3}{x^{2}-2x+3}$

5) $\frac{n^{2}-2n+2}{n^{2}-2n} - \frac{1+n}{n} = \frac{n-1}{n-2}$

6) $\frac{2x}{x^{2}-1} + \frac{2}{x+1} = \frac{2-x}{x^{2}-x}$