#### Question

If a : b = c : d, prove that: xa + yb : xc + yd = b : d.

#### Solution

Given `a/b = c/d`

`=> (xa)/(yb) = (xc)/(yd)` (Multiplying each side by x/y)

`=> (xa = yb)/(yb) = (xc + yd)/(yd)` (By componendo)

`=> (xa + yb)/(xc + yd) = (yb)/(yd)`

`=> (xa + yb)/(xc + yd) = b/d`

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Solution If a : B = C : D, Prove That: Xa + Yb : Xc + Yd = B : D. Concept: Componendo and Dividendo Properties.