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What sounds better? Is first version viable?

  1. This solution is quite difficult to come up with.
  2. It is quite difficult to come up with this solution.
  • while the rule is to not end a sentence with a preposition, that tends to be in writing more than in speech. Formal writing means following the rules, but we see and hear this in everyday speech and writing all the time. "Who are you going with?" Few of us would say or write that in any other way. Both of your examples are fine unless you are writing formally, like for a business report. – WRX Feb 24 '17 at 18:19
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The first is viable. If I were going to change it, it wouldn't be because of the "dangling preposition;" instead, I would use a more formal verb than "come up with" (such as derive):

This solution is quite difficult to derive.

I'm not saying there's anything wrong with come up with. There isn't. However, many so-called dangling prepositions are really nothing more than the last part of a phrasal verb, and that fact is worth pointing out. For example, consider these:

  • The oil rig fire was not easy to put out.
  • Last night, Maria and David decided to break up.
  • It was ten o'clock before the train finally showed up.

No one would even blink an eye if those sentences said:

  • The oil rig fire was not easy to extinguish.
  • Maria and David decided to end their relationship.
  • It was ten o'clock before the train finally arrived.

Your first sentence follows this same pattern; it uses come up with as a phrasal verb. In fact, in Macmillan's entry for this word, their example usage consists of a question with with at the end:

Is that the best you can come up with?

0

Both sentences sound equally good to me. If I were you, I wouldn't worry about the dangling preposition rule at all. Dangling prepositions are used frequently in everyday speech and even when writing formal essays. It's always seemed like a really pointless grammar rule to me, and it seems to be enforced very seldomly; dangling prepositions never really obscure the meaning of a sentence and it's a very commonplace way to speak.

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