If x: y =a: b, prove that a: x=(a+b): (x: y)

We start by writing the ratio  and  as fraction



This shows two pairs of equivalent fractions

and 

We will use the first pair of fraction
 ⇒ cross multiply gives
 ⇒ then rearrange
 ⇒ which we can also write in form of ratio


Hence it is proved that  as required