| \frac{-3}{x}+\frac{x-6}{x^2-2x}+\frac{x}{x^2-8x+12}=\frac{-x+12}{x^2-8x+12} | \frac{1}{x^2+x+1}+\frac{x^2+2}{x^3-1}=\frac{1}{x-1} |
| \frac{5}{x}+\frac{x+5}{x^2-x}-\frac{36x}{x^2+4x-5}=\frac{-30}{x+5} | \frac{-2}{x}+\frac{x-4}{x^2-2x}-\frac{x}{x^2-6x+8}=\frac{-2}{x-4} |
| \frac{3}{x}+\frac{x+15}{x^2-5x}-\frac{16x}{x^2+10x-75}=\frac{-12}{x+15} | \frac{1}{x^4+x^2+1}+\frac{x^4+2}{x^6-1}=\frac{1}{x^2-1} |
| \frac{2}{x}+\frac{x+6}{x^2-3x}+\frac{x}{x^2+3x-18}=\frac{4x+18}{x^2+3x-18} | \frac{1}{x^4+x^3+2x^2+x+1}-\frac{2}{x^4+x^2+1}=\frac{-1}{(x^2-x+1)(x^2+1)} |
| \frac{1}{x^4+x^3+x^2+x+1}+\frac{x^4+x^3+x^2+2}{x^5-1}=\frac{1}{x-1} | \frac{-5}{x}+\frac{x-5}{x^2-x}+\frac{x}{x^2-6x+5}=\frac{-3x+20}{x^2-6x+5} |
| \frac{2x+4}{x^2-1}+\frac{x+2}{x^2-3x+2}=\frac{3x+6}{x^2-x-2} | \frac{1}{4x^4+2x^2+1}+\frac{4x^4+2}{8x^6-1}=\frac{1}{2x^2-1} |