If p : q = r : s; then show that :

mp + nq : q = mr + ns : s.

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Solution

$p over q equals r over s fraction numerator m p over denominator q end fraction equals fraction numerator m r over denominator s end fraction fraction numerator m p over denominator q end fraction plus n equals fraction numerator m r over denominator s end fraction plus n fraction numerator m p plus n q over denominator q end fraction equals fraction numerator m r plus n s over denominator s end fraction s o space m p plus n q colon q equals m r plus n s colon s$

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