| \frac{1}{x^2+x+1}+\frac{x^2+2}{x^3-1}=\frac{1}{x-1} | \frac{-3}{x}+\frac{x-12}{x^2-4x}-\frac{4x}{x^2-16x+48}=\frac{-6}{x-12} |
| \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+25}{x^2-5x}+\frac{x}{x^2+20x-125}=\frac{7x+150}{x^2+20x-125} |
| \frac{3}{x}+\frac{x+12}{x^2-4x}-\frac{16x}{x^2+8x-48}=\frac{-12}{x+12} | \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{4}{x}+\frac{x+12}{x^2-3x}+\frac{x}{x^2+9x-36}=\frac{6x+60}{x^2+9x-36} | \frac{1}{x^4+x^2+1}+\frac{x^4+2}{x^6-1}=\frac{1}{x^2-1} |
| \frac{-5}{x}+\frac{x-25}{x^2-5x}-\frac{16x}{x^2-30x+125}=\frac{-20}{x-25} | \frac{2}{x}+\frac{x+6}{x^2-3x}+\frac{x}{x^2+3x-18}=\frac{4x+18}{x^2+3x-18} |
| \frac{1}{4x^4+2x^2+1}+\frac{4x^4+2}{8x^6-1}=\frac{1}{2x^2-1} | \frac{2x+4}{x^2-1}+\frac{x+2}{x^2-3x+2}=\frac{3x+6}{x^2-x-2} |