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Question
If `(5x + 7y)/(5u + 7v) = (5x - 7y)/(5u - 7v)`, show that `x/y = u/v`
Solution
`(5x + 7y)/(5u + 7v) = (5x - 7y)/(5u - 7v)`
Applying alternendo `(5x + 7y)/(5u + 7v) = (5x - 7y)/(5u - 7v)`
Applying componendo and dividendo
`(5x + 7y + 5x - 7y)/(5x + 7y - 5x + 7y) = (5u + 7v + 5u - 7v)/(5u + 7u - 5u + 7v)`
⇒ `(10x)/(14y) = (10u)/(14v)`
⇒ `x/y = u/v`
Hence proved. ...`("Dividing by" = 10/14)`
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