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Question
If `(3x + 4y)/(3u + 4v) = (3x - 4y)/(3u - 4v)`, then show that `x/y = u/v`.
Solution
We have
`(3x + 4y)/(3u + 4v) = (3x - 4y)/(3u - 4v) ...["Applying alternendo"]`
`(3x + 4y)/(3u - 4v) = (3x + 4y)/(3u - 4v)` ...[By componendo and dividendo]
`(3x + 4y + 3x - 4y)/(3x + 4y - 3x + 4y) = (3u + 4v + 3u - 4v)/(3u + 4v - 3u + 4v)`
⇒ `(6x)/(8y) = (6u)/(8v)`
⇒ `x/y = u/v`.
Hence proved.
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