Express 1(x−1)(x−2)\frac{1}{(x-1)(x-2)}(x−1)(x−2)1 as a partial fraction decomposition.
1x−2−1x−1\frac{1}{x-2} - \frac{1}{x-1}x−21−x−11
1x−1−1x−2\frac{1}{x-1} - \frac{1}{x-2}x−11−x−21
1(x−1)2+1(x−2)2\frac{1}{(x-1)^2} + \frac{1}{(x-2)^2}(x−1)21+(x−2)21
2x−1+3x−2\frac{2}{x-1} + \frac{3}{x-2}x−12+x−23