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Algebra
11 Feb 2012 14:57:35 IST
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13 Feb 2012 14:44:50 IST
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A componendo dividento is a good tool in reducing the number of steps in some problems.
it is actually
if
a/b=c/d
then
(a+b)/(a-b)=(c+d)/(c-d)
the proof is simple
a/b=c/d--------------(1)
adding 1 to both sides we get
(a+b)/b=(c+d)/d------------------(2)
similarly taking the reciprocal and subtracting from 1 we get
(a-b)/a=(c-d)/c--------------------------(3)
dividing (2) and (3)
we get
[(a+b)/(a-b)]*(a/b)=[c+d)/(c-d)]*c/d
since a/b=c/d
we can cancel to the the above result i.e
a/b=c/d
Hope you understand
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its nothing but a method in which a mixed fraction is converted nito a simple one