If a : b = c : d, prove that (9a + 13b) : (9a − 13b) = (9c + 13d) : (9c − 13d).
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If a : b = c : d, prove that (3a + 2b) : (3a − 2b) = (3c + 2d) : (3c − 2d).
If (3a + 5b) : (3a − 5b) = (3c + 5d) : (3c − 5d), prove that a : b = c : d.