Find the partial fraction decomposition of x2+1(x−1)2(x+1)\frac{x^2+1}{(x-1)^2(x+1)}(x−1)2(x+1)x2+1.
12(x−1)+1(x−1)2+12(x+1)\frac{1}{2(x-1)} + \frac{1}{(x-1)^2} + \frac{1}{2(x+1)}2(x−1)1+(x−1)21+2(x+1)1
1x−1+1(x−1)2+1x+1\frac{1}{x-1} + \frac{1}{(x-1)^2} + \frac{1}{x+1}x−11+(x−1)21+x+11
12(x−1)+1x−1+12(x+1)\frac{1}{2(x-1)} + \frac{1}{x-1} + \frac{1}{2(x+1)}2(x−1)1+x−11+2(x+1)1
14(x−1)+1(x−1)2+14(x+1)\frac{1}{4(x-1)} + \frac{1}{(x-1)^2} + \frac{1}{4(x+1)}4(x−1)1+(x−1)21+4(x+1)1