Sorry, you cannot just add the potential transfer speeds of different disks up and say "see, it's faster." It does not work like that, and transfer speeds are often not the relevant measure. (Note I'm referring here to a normal consumer machine, not some raid / mirroring configuration between the ssd and HDD).
First, it matters quite a lot what which files are where - if the files that are needed at any particular point for something important are on the slower drive, it simply WILL be slower - there's no 'additive' operation.
Second, the weak point of hard drives is not so much the transfer speeds, but the seek operation (physically moving the drive heads), which are quite a bit slower again than the transfer speed (compared to an SSD, where it's an electronic operation). Doesn't matter much for large files, but can matter a lot when reading and writing lots of small files (precisely those zillions of temp/cache files that are used a lot).
Now - mitigating on the other side is that for a lot of drive operations, it doesn't matter much - for one example, if you're playing a movie and it only needs 10mb/s and the drive can handle ten times that, mostly irrelevant. And of course, overall, if the computer's 'fast enough' and you don't notice any difference - that's also fine.
But it's pretty much unambiguous, SSD + HDD will usually not be faster (or only in very rare cases) than pure SSD or SSDX2 - and if files are poorly placed, could be worse (and potentially much worse). Putting files that are used a lot by the system (read and written) on the HDD instead of SSD is not the way to maximize speed (you woudln't want system swap on an HDD either).
Of course, if you do this and you're happy with it, fine - but it won't be faster.
I won't get into the 'ssd wear' issue - I think it's a false economy and mostly no longer relevant, but for those who want to believe it's worth giving up the speed for a few pennies of extra ssd longevity over years of use, by all means.
If by 'performance' you only mean speed, that first statement is not true (or not unambiguously true). Adding an HDD to an SSD system is mostly not going to increase speed.
BUT: that point does not contradict the second - there are lots of good reasons to have a system with a hard drive, LOTS of good reasons (more storage at less cost, backup, redundancy, and on and on. All of my systems except tiny laptop have ssd + hdd - and the tiny laptop uses network drives and an external for backups, too.
Again, I'm not advocating one should not use a hard drive. But if it's pure speed, SSDs only. Now personally I think pure speed only is a silly and not cost effective approach (hey, if that's what you want and you have too much money, put 1tb of RAM in your system for a ram drive and only use SSD/HDD for persistent data).
I did not make this claim. I think it is 'better' to have multiple drives, and for normal cost/benefit calcs, HDDs are extremely useful. A backup drive should always be there and a separate device (and HDD best bang for buck for backup). But I wouldn't claim that adding an HDD makes it faster, because it won't be true most of the time.
) the interesting news is that while talking to the tech guy whom was awesome (gave him a 10 on feedback) I mentioned I had four dead seagate HD"s he sent me a ticket I have 30 days to pack them up and send them in and they will recover my data and send it back to me.
