Discussion Forum—A Way with Words, a fun radio show and podcast about language

I would say it differently.   For machinery that's broken, yes, "fix" means "repair".   But a bed sheet isn't the same sort of thing; if I heard someone say "fix the bed sheet" I wouldn't think he meant to repair it, as if it were torn and you wanted me to mend it; if it were rumpled, I'd think you wanted me to straighten it.   Or if perchance we had it rigged as part of a larger mechanism—to cover a trap door, or to be used as an improvised filter for muddy water perhaps, and it got disarranged somehow, you might tell me to "fix" it meaning to put it back in working order.

We also say "fix your hair", meaning it's disheveled and it should be straightened out; or "fix your clothes", possibly meaning they're disheveled or just that they don't cover you properly.

We also speak of "fixing" a relationship, say a marriage.

An older meaning for "fix" is to fasten it in place—to "fix" A to B would definitely mean to fasten A to B—but you don't hear that much nowadays.   In that sense it's probably an abbreviation of "affix".

To fix something up is closely related.   No doubt you already understand that you can add "up" to many verbs to intensify their meaning; if you burn up a house it's just another way of saying you burn it completely, for example.   So you can say a car was broken and you fixed it up again.   But there are a few other ways to use it:

If a place you live in is in disrepair—not necessarily broken, but even if it's just dirty, with a few rotting timbers, paint peeling, windows broken and so forth—to "fix up" that house (or boat or whatever) means to make general repairs.   It may not mean to make it perfect, just to make it better.   A "fixer-upper", in fact, is a house that needs many minor repairs; I know people who like to buy a house in poor condition, spend their weekends fixing it up and then sell it a year or three at a profit.

To "fix up" two people means to introduce a man and a woman to each other, with the idea that they might like each other, and eventually fall in love and marry.   Or you can "fix Harry up with Sally", which means the same thing.

So I guess I would say that you can "fix" a specific problem, or you can "fix" an object that has a particular problem; but if you're "fixing it up" it probably has several small problems rather than one particular one.

The American Heritage Dictionary makes this interesting point about fixin' to do (Southernese for 'on the verge of doing'), how its correct context is so finely delineated:
(verbatim in the interest of non-commercial discussion)
...They were fixing to leave without me. Semantically, fixing to can refer only to events that immediately follow the speaker's point of reference. One cannot say, "We're fixing to have a baby in a couple of years."