#### Question

If a : b = c : d, prove that: (9a + 13b) (9c – 13d) = (9c + 13d) (9a – 13b).

#### Solution

Given `a/b = c/d`

`=> (9a)/(13b) = (9c)/(13d)` (Multiplying each side by 9/13)

`=> (9a + 13b)/(13a - 13b) = (9c + 13d)/(9c - 13d)` (By componendo and divdendo)

`=> (9a + 13b)/(13a - 13b) = (9c + 13d)/(9c - 13d)` (By componendo and divdendo)

`=> (9a + 13b)(9c - 13d) = (9c + 13d)(9a - 13b)`

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Solution If a : B = C : D, Prove That: (9a + 13b) (9c – 13d) = (9c + 13d) (9a – 13b). Concept: Componendo and Dividendo Properties.