| \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^2+1}+\frac{x^4+2}{x^6-1}=\frac{1}{x^2-1} |
| \frac{2}{x}+\frac{x+4}{x^2-2x}-\frac{9x}{x^2+2x-8}=\frac{-6}{x+4} | \frac{3}{x}+\frac{x+9}{x^2-3x}-\frac{16x}{x^2+6x-27}=\frac{-12}{x+9} |
| \frac{1}{x^2+x+1}+\frac{x^2+2}{x^3-1}=\frac{1}{x-1} | \frac{5}{x}+\frac{x+10}{x^2-2x}-\frac{36x}{x^2+8x-20}=\frac{-30}{x+10} |
| \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} |
| \frac{-5}{x}+\frac{x-20}{x^2-4x}+\frac{x}{x^2-24x+80}=\frac{-3x+80}{x^2-24x+80} | \frac{4}{x}+\frac{x+16}{x^2-4x}+\frac{x}{x^2+12x-64}=\frac{6x+80}{x^2+12x-64} |
| \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{-3}{x}+\frac{x-15}{x^2-5x}+\frac{x}{x^2-20x+75}=\frac{-x+30}{x^2-20x+75} |