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Is it grammatically correct to say "better able to" or "able to better"?

This applies to any usage I can think of, but the sentence that prompted this question is:

Users are [phrase] understand and improve their health.

Which is correct?
Users are better able to understand and improve their health.
Users are able to better understand and improve their health.


When I attempt to break down the sentence and think about each part, both uses seem as though they are technically correct. Both are saying that the users are able to understand and improve their health more so than before.

It almost reminds me of the distributive rule in math. Both are saying something is able to be done, and both are adding a qualifier to the something that is able to be done.

Better able to something == better(  able to( something ) )
Able to better == able to( better( something ) )

Is "better able to" like saying something was able to be done before, but now it is easier to do; while "able to better" like saying something wasn't able to be better done before, but now it is?


Regardless of my rambling thoughts, which is correct?

Should you say:

"Users are able to better understand and improve their health."

or

"Users are better able to understand and improve their health."

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Your mention of the Distributive Property piqued my interest. Consider the two cases presented:

Users are able to better understand and improve their health.

Users are better able to understand and improve their health.

Using your notation above, I see this:

able to (better understand and improve health) == able to better understand and able to improve health

better able to (understand and improve health) == better able to understand and better able to improve health

Depending on the position of better, it modifies either the word understand, or the phrase able to. In the first case, only the user's understanding is made better, and this increased understanding is inferred as a cause of the user's improved health. In the second case, both the user's understanding and capacity to improve health are made better. It's a small distinction, but it is there.

As for which is correct, it depends on where you want the emphasis of the word better. Do you only want it to apply to understanding, or to capacity for improved health as well?

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I think the preferred phrase would depend on the subject and its context, though considering their similarity people are going to conflate them and use them interchangeably anyway.

a) able to better phrase: Consider an excerpt of

The tricorder is a great invention. Users are able to better understand ...

which has the meaning that users (of some product or service) gain a higher level of understanding.

b) better able phrase would connote the comparative abler, so it should be more valid in a case such as

The graphical display of results is less confusing than the columns of numbers used to be. Users are better able to understand ...

Here the users find it easier to understand something, but the final level of understanding might be same other than effort required to parse the data.

However, note that Google n-gram shows the second form is used way more often. I wonder whether this is the right usage of find something easier (more able) to do, or used to indicate that that something can be done better (to a greater extent) as in case (a).

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"To understand" is an infinitive verb. Placing "better" between the two elements of an infinitive creates a split infinitive, which is grammatically incorrect. If you wish to modify the infinitive verb, you must place the modifier before or after, but not in the middle, of the verb.

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