To use prepositions or not?

Question

The sentence :

A dog has no trouble knowing where to scratch itself to kill a flea.

I think below sentences are more familiar to my mind where a preposition comes after the trouble.

1. A dog has no trouble with/in/of knowing where to scratch itself to kill a flea.

However, It seems the first sentence is a reduced relative clause. It means we can rewrite the sentence as below:

A dog has no trouble ( that it is knowing ) where to scratch itself to kill a flea.

Under this considerations, my question is why the author preferred to use or choose reduced relative clause rather to use a preposition? If these scenarios convey different meanings in a Native person (or a person expert in English )? The sentence has been driven from an academic text. Can we say using relative clauses are more preferable in academic or formal English ?

Answer 1

To have { trouble / difficulty / a problem } doing X and to have { trouble / difficulty / a problem } with doing X are related expressions with somewhat different senses.

• I have { trouble / difficulty / a problem } doing X means that it is not easy for me to do X. The subject of have is identical with the subject of doing and is always omitted.

  I have trouble waterboarding prisoners = Waterboarding prisoners is difficult for me; I haven't mastered the technique.

  In this idiom the doing piece is not a relative clause of any kind; it is a participle clause acting as complement of the noun { trouble / difficulty / a problem } expressing what activity is difficult.

• I have { trouble / difficulty / a problem } with doing X often (I'm going to qualify this in a minute) means that doing X troubles me, makes me uneasy: I have practical or moral objections to doing X. Have and doing may have different subjects, and if the subject of doing is omitted it implies that the subject is 'generic':

  I have trouble with waterboarding prisoners = For anybody to waterboard prisoners troubles me.

  In this idiom the doing piece is a gerund clause acting as object of the preposition with. The preposition phrase with doing X is, again, a complement of the preceding noun.

  Note that this idiom may use nominals of other sorts, too:

  • I have a problem with torture of any kind.

  Moreover, the senses are so similar that the line I have just drawn is not at all a strict one. We often use the second idiom, the one with the preposition phrase, in the same sense as the first one.

  I have trouble with solving quadratic equations.
  I have a problem with my eyesight.

  Which sense is intended is generally evident from the context.

  The first idiom is not, in my experience, used with the sense of the second.