Question

Resolve $\frac{1}{{(x-1)}^2(x-2)}$ into partial fractions.

Answer 1

$\frac{1}{(x-1{)}^2(x-2)}$
$=\frac{(x-1)-(x-2)}{(x-1{)}^2(x-2)}$
$=\frac{1}{(x-1)(x-2)}-\frac{1}{(x-1{)}^2}$
$=\frac{(x-1)-(x-2)}{(x-1)(x-2)}-\frac{1}{(x-1{)}^2}$
$=\frac{1}{x-2}-\frac{1}{x-1}-\frac{1}{(x-1{)}^2}$