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ax²+(b+ac)x +bc by x+c

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

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