Hello

$\displaystyle (x-a)(x-b) / (c-a)(c-b) + (x-a)(x-c) / (b-a)(b-c)$

$\displaystyle = (x-a)(x-b)(b-a) - (x-a)(x-c)(c-a) / (c-a)(c-b)(b-a) $

My textbook suggests the absence of $\displaystyle (b-c)$ in the denominator is accounted by the fact that $\displaystyle b-c = -(c-b) $. I understand this to imply that $\displaystyle (c-b)$ and $\displaystyle (b-c)$ cancel each other out. Yet the denominator is absent only of $\displaystyle (b-c)$. $\displaystyle (c-b)$ is still there. Would someone please help me understand what's going on here?