If a : b = c : d, prove that :
xa + yb : xc + yd = b : d
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5a + 7b : 5a - 7b = 5c + 7d : 5c - 7d
If (7a + 8b)(7c - 8d) = (7a - 8b)(7c + 8d);
prove that a : b = c : d.