In the above solution you have given r3=ar2+br1/a+b. Why you have not written it as r3=ar1+b+r2/a+b?

It is based on a formula in mathematics called the Internal-section formula.

 

According to this when a point divides a segment internally in the ratio a:b then the coordinates of that point are given by crossed numbers.

 

Here, we do not have coordinates by direct dimensions. So, a will be multiplied by r₂ and b by r₁.

 

Hope this cleared your doubt. If not, then please let us know.