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Question
If (xa + yb) : b :: (xc + yd) : d, prove that a : b :: c : d.
Theorem
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Solution
⇒ (xa + yb) : b :: (xc + yd) : d
⇒ `(xa + yb)/b = (xc + yd)/d`
⇒ `(xa)/b + (yb)/b = (xc)/d + (yd)/d`
⇒ `x a/b + y = x c/d + y`
⇒ `x a/b = x c/d`
⇒ `a/b = c/d`
⇒ a : b :: c : d
Hence proved.
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