Find the partial fraction decomposition of fracx2+1x(x−1)2\\frac{x^2 + 1}{x(x-1)^2}fracx2+1x(x−1)2.
frac−1x+frac1x−1+frac2(x−1)2\\frac{-1}{x} + \\frac{1}{x-1} + \\frac{2}{(x-1)^2}frac−1x+frac1x−1+frac2(x−1)2
frac1x−frac1x−1+frac2(x−1)2\\frac{1}{x} - \\frac{1}{x-1} + \\frac{2}{(x-1)^2}frac1x−frac1x−1+frac2(x−1)2
frac−1x+frac2x−1+frac1(x−1)2\\frac{-1}{x} + \\frac{2}{x-1} + \\frac{1}{(x-1)^2}frac−1x+frac2x−1+frac1(x−1)2
frac1x+frac1x−1−frac2(x−1)2\\frac{1}{x} + \\frac{1}{x-1} - \\frac{2}{(x-1)^2}frac1x+frac1x−1−frac2(x−1)2