Can you please explain componendo-dividendo method

Question

Ravi · Answer

If a:b=c:d ...(Numerator/Denominator=N/D)
i.e. a/b=c/d

Applying Cand D would be
N/D=(N+D)/(N-D)

i.e. (a+b)/(a-b)=(c+d)/(c-d)

Eg.
Let a/b=k

Adding 1 both sides
(a/b)+1=k+1
(a+b)/b=k+1 ...(i)

Similarily, by subtracting 1 both sides (a/b)-1=k-1
(a-b)/b=k-1 ...(ii)

Dividing eqns i and ii

We get,
(a+b)/(a-b)=(k+1)/(k-1)

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Can you please explain componendo-dividendo method

Can you please explain componendo-dividendo method

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