Multifluid manometer (pressure problem)

[yecko]

Homework Statement

In the image, as the first chapter of thermodynamics class, I understand all things in the answer except the highlighted part (lower bottom of the image). It is not directly related to thermodynamics but about the area ratio of the two ends of the tube, but I do not understand why is the equation formed this way.
Δh (which is a decrease) should be only there in the right tube as indicated, why is it a sum of Δh of both left and right? why Δh(Hg,left)=Δh(Br) and Δh(Hg,right)=Δh(Br)*A2/A1 as well?
Thank you very much for any help!

(http://i.imgur.com/1Pjks2P.png )

2. Homework Equations
(In the image)

The Attempt at a Solution

(In the image)

 

[haruspex]

You need to interpret the definitions of the Δh terms correctly, which may not be entirely clear.
Δh_Hg is defined as the difference in the heights of the mercury in the left and right columns. If the height in the right column drops by Δh_br then the height in the left column rises by (A₂/A₁)Δh_br, so the difference in the two mercury levels increases by the sum of those two changes.