The fuel trim reacts to many things. First off, no 2 injectors have the same flow. If the average flow of the 3 injectors on one bank in slightly higher than the DME is programmed for, then the LTFT will show a negative number on a normally running engine. If the average flow is less than expected, the LTFT will show a positive number. This is all in an attempt to get the fuel injection to what the DME wants.
Basic Operation:
The engine is started and the DME injects a specfic amount of fuel into the cylinders based on what it learned and stored in the LTFT tables the last time the engine was run. When the engine warms up and goes into CLOSED LOOP, This is what happens:
The MAF tells the computer how much air is being ingested and the DME tells the injectors to inject the amount of fuel necessary to bring the air/fuel ratio to 14.5:1. THIS CALCULATION TAKES INTO ACCOUNT THE SETTINGS OF THE LTFT. Next, the air/fuel ratio is measured from the exhaust by the O2 sensor which will make an adjustment to the STFT to either increase or decrease the amount of fuel injected. This continues and after awhile, the STFT adjustment is transfered to the LTFT tables and the STFT returns to ZERO until further adjustment is necessary.
ie. If your engine is running lean, the O2 sensor will increase the STFT by a specific amount; let's say 10%. If this increase continues for awhile, the 10% increase will transfer to the LTFT and the STFT will be ZERO. This is necessary, because a car that is started cold looks at the LTFT for what amount of fuel to use above what the DME is programmed for. In this example, if this table was not set, you would be running lean until the car warmed up and the O2 sensors could control fuel again.
My car has a drastically different LTFT setting for each bank. Because I am using large injectors and therefor the flow is much more than stock, my LTFT currently read: Bank 1 -18% and Bank 2 -9.8 %. This simply means that bank 1 injectors flow more than do bank 2 and that the flow of moth banks is more than necessary for normal vehicle operation. Both are well within the -25%/+25 threshold.
The P1123 and P1125 errors really have nothing to do with the fuel trim, but only with the voltage readings of the O2 sensors. The allowable voltage of the sensors is between .01 and .9 volts. If the sensor goes outside this range, a code is generated. The voltage goes lower when the fuel/air mixture is lean and goes high when it is rich. This voltage change directly effects and changes the STFT only. Higher voltage will decrease the STFT and lower will reduce it. Apparently the sensor went beyond their upper voltage limit and caused the codes.
You have to remember that many of the computer generated codes do not give you the underlying cause for the error, but only a place to start looking. You CAN conclude tho, that these codes are accurate in the reporting of the operation of the O2 sensors. Therefore, because they exceeded their LEAN threshold (high voltage limit) Either the sensors are bad, or they are reading a rich mixture accurately but cannot adjust enough. So you eliminate bad sensors and then simply go through the old fashion steps of determining the many things that can cause an engine to run rich and eliminating them as the cause, one by one.
Sorry for the long reply...it must be the laxative I took earlier. Hope it make sense.