this will be long.so bare with me.
the SYNTH'S eidolon is a "suit" of sort. you have to remove ALL of it's temp hp before you even get to the character's, so make sure he keeps the rage "temp" hp and the eidolon's seperete.
notice ability increase tothe synth will increase only the synth's hp not the eidolon's temp hp (ee the link at bottom underthe heading "Summoner: What happens when a synthesist (page 80) takes ability damage or drain while the eidolon is present?")
the eidolon only count it normal con for its max temp hp.
more then that the rage hp ARE NOT TEMP HP.temp hp are like expandable hp that while they are there are removed first and after the effect that made them goes away if there were any left they are just gone and the character is left with its own hp.
rage hp come form increase to con. which increae booth max and curent hp by levelX con bonus gained (normal rage increase con by 4 so con obnus is +2 higher = 2Xlevel) but when the rage is over the same amount goes out from corent and max hp as well. that mean that a level 13 toon will gain +26 hp when noramly raging and loose 26 when he gets his con back to normal. if in the midwhile he lost hp they are not removed from this sum.
example:
a 100 hp toon wiht +26 hp from TEMP source(for 100 hp +26 temp hp).like from a spell is hit for 30 damage before spell end. the toon has now 96 hp.
same 100 hp toon gaining 26 hp to max and curent hp via raging will have a max of 126 hp while raging. if he takes 30 damage his curent hp drop to 96. when rage end he loses 26 more hp since his con got down 4 points so now he has 70 hp (yes this mean that every rager that is hit too much might find himself DEAD when the rage ends and his extra hp go away.if said toon was lowered to 2 hp and had a normal con of 22 before raging when the rage will be over his total hp take a -26 and he'll drop to -24 hp = dead man walking).
-again all this damage is only taken if the eidolon suit is at 1 hp so any more damage is syphoned through the character's hp with his "Fused Link (Su)" .do note. he can not ,unless using "life conduit" spell, move hp from himslef to his suit BEFORE the suit reachs it last 1 temp hp.he WILL WANT to take damage instead of the suit as the suit can not be CURED and he can(see more about this ahead)
also note. the eidolon hp ARE temp hp. meaning you can not CURE them with noraml spells and not even wit hthe fast healing evolution !!!
it was ruled in the Q&A that only spells and effects that specificly mantioned healing the eidolin. souch as rejuvinate eidolon (which restore it's temp hp) and Life Conduit (which let the character trade his hp,that CAN be healed via cure spells, and the eidolons temp ones).
also if the eidolon is lowered to 0 hp when it is called again it has 1 hp (if it is sent away with morethen one hp it comes back wit hthe amount it had when it was sent away.)
see more inforamtion here: look at all this page
edit ( i can't seem to be able to re-edit my post from above)
the link in the 1st part should have been this one
still i made a mistake it doesn't' say temp increase to the fused form doesn't add to the temp hp of the eidolon.
let me try and make it easier for you tho:
1st thing you must take full account for both the synth with and without the eidolon suit. i keep calling it a suit because that is what it is. it has no int\cah\wis meaning it is not alive like other summoners pets. this is some kind of an outsider buff. it can be banished. and if the summoner sleep it goes away, but it has no skills\feat\saves of its own.
so keep track of the characters hp str\dex\con without the suit. that is the normal toon. but once he fuses he replaces his str\con\dex with the eidolons's(which also mean that inheret bonus and abilities he increases with HIS 4th level advancement do not show up in the fused form unless they are mental abilities.
next take account of the eidolon's hp. notice that the suit has LOWER hd then the character(even full classed summoner have more hd then their eidolon it doesn't get a hd for each level. let alone this multi classed character) at level 10 summoner his eidolon has 8 hd. this is important since when he rage his own hp gain 2X his hd(13 so 26 hp) but the suit has only 8 hd so only 16 more temp hp. and when the rage ends both his and the temp hp lose said added hp (so his lower by 26 hp and the suit by 16).
now have it listed player hp: XXX. when raged gain 2Xlevel (so 26 now)
suit temp hp has : yyy when raged gain +2Xhd (so 8X2=16).
when raqe goes down so does this added hp.
any damage while raged is taken form the normal amount (temp hp first if fused).
last thing. most GM don't allow synths. and it is banned in Pathfinder's organized play campaign. (read the fyi fyi.
those that do allow them usually house-rule that when creating the toon he can not start with any attribute under 10 before racial adj. so to avoid the old 3-str/3-dex/3-con/18-wis/18-int/18-cha that turn into 27/27/27/18/18/20 when fused.
and remember that whatever ability he gains from an other class. if it is powered by class level it is only affected by that other class level. so this build barbarian's "Invulnerability (Ex)" uses ONLY the barbarian class level to count his damage reduction (1 for each 2 levels that make is 1 point of damage reduction. i had met gm who didn't notice that and had 2 levels of barbarian 18 wizard roam around with 10/-- dr )
