Question

If `a/b = c/d,` show that (9a + 13b) (9c - 13d) = (9c + 13b) (9a - 13d).

Answer 1

We have `a/b = c/d`  
`[ "Multiplying both sides by" 9/13]`
`(9a)/(13b) = (9c)/(13d)`
[By componendo and dividendo]
`(9a + 13b)/(9a - 13b) = (9c + 13d)/(9c - 13d)`
(By cross multiplication)
(9a + 13b) (9c - 13d) = (9a - 13b) (9c + 13d).
Hence proved.