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I still have a lot of problems to distinguish when the word "that" can result unnecessary.

Take these two sentences for example:

-These results indicate that the adsorption of PVA on the surface was promoted by using HCl as doping agent.

-These results indicate the adsorption of PVA on the surface was promoted by using HCl as doping agent.

Which is correct and which is not?
Which sound better?
Is there a preference for native English speakers?

Please consider that this is formal English for scientific purposes.

Thanks
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In a scholarly article I'd be inclined to use "that".

CJ
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Additionally, here's a source that might help:

Theodore Bernstein author of Dos, Don'ts & Maybes of English Usage (Gramercy Books: New York. 1999. p. 217) lists three conditions in which we should maintain the conjunction that:

1) When the verb of the clause is long delayed:

"Our annual report revealed that some losses sustained by this department in the third quarter of last year were worse than previously thought."

(Notice the distance between the subject "losses" and its verb, "were.")

Compare:

These results indicate that the adsorption of PVA on the surface was promoted by using HCl as doping agent.

(Notice the distance between the subject "absorption" and its verb "was promoted.")

Is "that" worth keeping or not? (Good question)

Read more here: http://www.ccc.commnet.edu/grammar/conjunctions.htm#that

(scroll down to where it says, "Omitting that")