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# If a : B = C : D, Prove That: (9a + 13b) (9c – 13d) = (9c + 13d) (9a – 13b). - Mathematics

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#### 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)(9c - 13d) = (9c + 13d)(9a - 13b)

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