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Class 10 > Learn Mathematics > If (3a + 4b) / (3c + 4d) = (3a - 4b) / (3c - 4d), prove...
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If (3a + 4b) / (3c + 4d) = (3a - 4b) / (3c - 4d), prove that a / b = c / d?

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9a:8b=9c:8d (by compnendo and dividendo).
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(3a+4b)(3c-4d)=(3a-4b)(3c+4d) 9ac-12ad+12bc-16bd=9ac+12ad-12bc-16bd -24ad=-24bc ad=bc a/b=c/d.
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(3a + 4b) / (3c + 4d) = (3a - 4b) / (3c - 4d), (3a + 4b) / (3a - 4b) = (3c + 4d) / (3c - 4d),........(1) By adding 1 from the both sides, (6a) / (3a - 4b) = (6c) / (3c - 4d),........(2) By subtracting 1 from the both sides, (8b) / (3a - 4b) = (8d) / (3c - 4d),..........(3) By dividing equation (2)...
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(3a + 4b) / (3c + 4d) = (3a - 4b) / (3c - 4d), (3a + 4b) / (3a - 4b) = (3c + 4d) / (3c - 4d),........(1) By adding 1 from the both sides, (6a) / (3a - 4b) = (6c) / (3c - 4d),........(2) By subtracting 1 from the both sides, (8b) / (3a - 4b) = (8d) / (3c - 4d),..........(3) By dividing equation (2) by equation (3), (6a/8b)=(6c/8d)...........(4) Hence a / b = c / d (By multiplying by 8/6 on the both sides in equation (4)) Proved a / b = c / d read less
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