# Math Help - Partial Fraction

1. ## Partial Fraction

so I have

x^2 / (x-1)(x-2)

The answer is 1 - 1/(x-1) + 4/(x-2).

Where did the 1 come from. I did the whole solving for A and B thing and got the same answer without the 1.

Thanks.

2. $\frac {x^2}{(x-1)(x-2)}=\frac {x^2}{x^2-3x+2}= 1+\frac{3x-2}{x^2-3x+2}=1+\frac{3x-2}{(x-1)(x-2)}$
now resolve $\frac{3x-2}{(x-1)(x-2)}$ into partial fraction
$\frac{3x-2}{(x-1)(x-2)}=\frac{- 1}{(x-1)} + \frac{4}{(x-2)}$
$therefore\quad \frac {x^2}{(x-1)(x-2)}=1-\frac{ 1}{(x-1)} + \frac{4}{(x-2)}$