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Question
If a : b : : c : d, prove that `(5a + 11b)/(5c + 11d) = (5a - 11b)/(5c - 11d)`
Solution
∵ a : b : : c : d
∴ `a/b = c/d`
⇒ `(5a)/(11b) = (5c)/(11d)` ...(Multiplying by `5/11`)
Applying componendo and dividendo,
`(5a + 11b)/(5a - 11b) = (5c + 11d)/(5c - 11d)`
⇒ `(5a + 11b)/(5c + 11d) = (5a - 11b)/(5c - 11d)` ...(Applying alternendo)
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