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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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