$a c x^{2} + (b c + a d) x + b d b y (a x + b)$

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Solution

$a c x^{2} + (b c + a d) x + b d b y (a x + b)$

$a c x^{2} + b c x + a d x + b d$

$= a c x^{2} + b c x + a d x + b d$

$= c x (a x + b) + d (a x + b)$

$= (a x + b) (c x + d)$

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

$= c x + d$

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