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"differentiate the two" is correct and can be used in written English.
It is commonly used when discussing or comparing two similar things or concepts, and means to identify or point out the differences between the two. Example: Can you differentiate the two breeds of dogs? In this sentence, the speaker is asking someone to explain or identify the differences between two types of dogs.
Exact(60)
Differential agar plates were used to differentiate the two organisms.
When a similar item has been mentioned previously, speakers tend to elaborate their referring expression in order to differentiate the two items, a phenomenon called lexical differentiation.
The Tories see these as "staged smash-ups" designed to differentiate the two parties.
And the visual scheme, which could have helped differentiate the two stories, is virtually identical.
On the issues, there was little to differentiate the two men.
This process, called subtractive hybridization, enables scientists to identify, and later to clone the fragments that differentiate the two species.
Keeping the beard (which was quite comely) might have been a good way to differentiate the two, at least visually.
The relationship between private and public spaces helps to differentiate the two types of publications".
The scientific method remains the best tool we have to differentiate the two.
A questionnaire to healthcare workers showed that none of the respondents knew how to differentiate the two clinical stages of trypanosomiasis.
Heck, even we were struggling to differentiate the two.
More suggestions(17)
distinguishes the two
discrimination the two
demarcate the two
disperse the two
identify the two
segregate the two
diversify the two
delineate the two
discriminate the two
differentiating the two
be distinguished the two
differentiate the 2
differentiate the both
discern the two
distinguishing between the two
distinguish the two
distinguishing the two
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com