If 5x+6y5u+6v=5x-6y5u-6v; then prove that x : y = u : v. - Mathematics

If `(5x + 6y)/(5u + 6v) = (5x - 6y)/(5u - 6v)`; then prove that x : y = u : v.

Sum

`(5x + 6y)/(5u + 6v) = (5x - 6y)/(5u - 6v)` ...(By aletrnendo)

`(5x + 6y)/(5x - 6y) = (5u + 6v)/(5u - 6v)`

`(5x + 6y + 5x - 6y)/(5x + 6y - 5x + 6y) = (5u + 6v + 5u - 6v)/(5u + 6v - 5u + 6v)` ...(By componendo and dividendo)

`(10x)/(12y) = (10u)/(12v)`

`x/y = u/v`

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