Find the partial fraction decomposition of x2+2x+3(x−1)(x2+x+1)\frac{x^2+2x+3}{(x-1)(x^2+x+1)}(x−1)(x2+x+1)x2+2x+3.
2x−1−xx2+x+1\frac{2}{x-1} - \frac{x}{x^2+x+1}x−12−x2+x+1x
2x−1+x−1x2+x+1\frac{2}{x-1} + \frac{x-1}{x^2+x+1}x−12+x2+x+1x−1
1x−1+1x2+x+1\frac{1}{x-1} + \frac{1}{x^2+x+1}x−11+x2+x+11
2x−1−x+1x2+x+1\frac{2}{x-1} - \frac{x+1}{x^2+x+1}x−12−x2+x+1x+1