Practice problem
Use partial fraction decomposition. x3+2x2+3x+4(x+1)(x2+x+5)2\frac{x^3+2x^2+3x+4}{(x+1)(x^2+x+5)^2}(x+1)(x2+x+5)2x3+2x2+3x+4
1/16x+1+−116x+1x2+x+5+−14x−3(x2+x+5)2\frac{1/16}{x+1}+\frac{-\frac{1}{16}x+1}{x^2+x+5}+\frac{-\frac{1}{4}x-3}{(x^2+x+5)^2}x+11/16+x2+x+5−161x+1+(x2+x+5)2−41x−3
2/25x+1+−225x+1x2+x+5+−25x−3(x2+x+5)2\frac{2/25}{x+1}+\frac{-\frac{2}{25}x+1}{x^2+x+5}+\frac{-\frac{2}{5}x-3}{(x^2+x+5)^2}x+12/25+x2+x+5−252x+1+(x2+x+5)2−52x−3
3/36x+1+−336x+2x2+x+5+−12x−4(x2+x+5)2\frac{3/36}{x+1}+\frac{-\frac{3}{36}x+2}{x^2+x+5}+\frac{-\frac{1}{2}x-4}{(x^2+x+5)^2}x+13/36+x2+x+5−363x+2+(x2+x+5)2−21x−4
4/49x+1+−449x+2x2+x+5+−47x−4(x2+x+5)2\frac{4/49}{x+1}+\frac{-\frac{4}{49}x+2}{x^2+x+5}+\frac{-\frac{4}{7}x-4}{(x^2+x+5)^2}x+14/49+x2+x+5−494x+2+(x2+x+5)2−74x−4
Type a concept, like “slope” or “photosynthesis”.
