Question

(x-b)$\frac{(x-b)^{2}+c(x-b)}{x-b+c}$

Answer 1

$\frac{(x-b)[(x-b)+c]}{x-b+c}=\\\\\frac{(x-b)(x-b+c)}{x-b+c}=\\\\\boxed{x-b}$