First of all, notice that final clauses with um ... zu require the subject of the main clause and the implicit subject of the infitivie clause to be the same.1, 2, 3, 4, 5 As an example, consider the sentence:
Ich brauche Zeit, um Deutsch zu lernen.
Here, both subjects are ich ("ich brauche Zeit" and "ich lerne Deutsch"). Now, consider the sentence:
Das Leben ist zu kurz, um Deutsch zu lernen.
Here, the subject of the main clause is das Leben ("das Leben ist zu kurz"), whereas the implicit subject of the infinitive clause is ich or man ("ich lerne Deutsch" or "man lernt Deutsch"). In standard German, the sentence is considered wrong; but you may hear or read such uses of um ... zu in spite of incongruent subjects in colloquial speech.
Some alternatives are the following sentences:
- Das Leben ist zu kurz, als dass man Deutsch lernen kann. (indicative)
- Das Leben ist zu kurz, als dass man Deutsch lernen könne. (subjunctive I)
- Das Leben ist zu kurz, als dass man Deutsch lernen könnte. (subjunctive II)
- Das Leben ist zu kurz zum Deutschlernen. (nominalization)
It is a matter of style, rather than of correctness, which alternative is preferrable. Purists would insist that als dass should be used with subjuctive I rather than with indicative. Still others might argue that, due to the irreal mood, only subjunctive II were correct.6
I prefer the latter, succinct alternative; and I dare to assert that—at least in spoken German—it occurs more frequently than the other ones.
Sources:
1 LEOs deutsche Grammatik
2 deutsch.info
3 deutschplus.net
4 learngerman.dw.com
5 lerngrammatik.de
6 LEOs deutsche Grammatik
Deutschlernen. I'm just surprised about my "observation". See https://german.stackexchange.com/q/7832/36160 for a question about "leichte Sprache". – Shegit Brahm May 21 '19 at 13:39