partial fractions

[heady veldt]

as in, why can't we express the right hand sign fraction as A/(x-1) + B/(x-1) + C/(x-2) instead?

<@&791435371564892232>

[worn inlet]

well A/(x-1) + B/(x-1) = something/(x-1) + something/(x-1) = (something else)/(x-1)