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Question Number 206452 by langatfredrick last updated on 15/Apr/24

Answered by A5T last updated on 15/Apr/24

If remainder means ∣x−y∣, then:  (t_x /x)=x;(t_y /y)=y⇒t_(∣x−y∣) =∣t_x −t_y ∣=∣x^2 −y^2 ∣  ⇒(t_(∣x−y∣) /(∣x−y∣))=∣x+y∣=x+y

$${If}\:{remainder}\:{means}\:\mid{x}−{y}\mid,\:{then}: \\ $$$$\frac{{t}_{{x}} }{{x}}={x};\frac{{t}_{{y}} }{{y}}={y}\Rightarrow{t}_{\mid{x}−{y}\mid} =\mid{t}_{{x}} −{t}_{{y}} \mid=\mid{x}^{\mathrm{2}} −{y}^{\mathrm{2}} \mid \\ $$$$\Rightarrow\frac{{t}_{\mid{x}−{y}\mid} }{\mid{x}−{y}\mid}=\mid{x}+{y}\mid={x}+{y} \\ $$

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