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Question
If a : b :: c : d, show that (2a + 3b) : (2c + 3d) :: (2a − 3b) : (2c − 3d).
Theorem
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Solution
a: b :: c : d
`a/b = c/d`
⇒ `(2a)/(3b) = (2c)/(3d)` ...[Multiplying both side `2/3`]
Apply Componendo and Dividendo
`(2a + 3b)/(2a - 3b) = (2c + 3d)/(2c − 3d)`
⇒ `(2a + 3b)/(2c + 3d) = (2a − 3b)/(2c − 3d)`
Hence prove.
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