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If A:B :: C:D :: E:F, Then Prove that (Ae + Bf)/(Ae - Bf) = (Ce + Df)/(Ce - Df) - ICSE Class 10 - Mathematics

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Question

If a : b :: c : d :: e : f, then prove that `("ae" + "bf")/("ae" - "bf")` = `("ce"  + "df")/("ce"  - "df")`

Solution

`"a"/"b" = "c"/"d" = "e"/"f"`

`"a"/"b" xx "e"/"f" = "c"/"d" xx "e"/"f"`

`=> ("ae")/("bf") = "ce"/"df"`

Applying componendo and dividendo 

`("ae + bf")/("ae - bf") = ("ce + df")/("ce - df")`

Hence , proved.

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APPEARS IN

 Frank Solution for Frank Class 10 Mathematics Part 2 (2016 to Current)
Chapter 9: Ratio and Proportion
Exercise 9.3 | Q: 6

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Solution If A:B :: C:D :: E:F, Then Prove that (Ae + Bf)/(Ae - Bf) = (Ce + Df)/(Ce - Df) Concept: Componendo and Dividendo Properties.
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