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The phrase "a simple extension of" is correct and usable in written English.
It can be used when describing something that adds to or builds upon an existing idea or concept in a straightforward manner.
Example: "This new feature is a simple extension of the previous version, enhancing its functionality without complicating the user experience."
Alternatives: "a straightforward addition to" or "an easy expansion of".
Exact(59)
The world of digital cellular phones, however, is rapidly becoming a simple extension of the world of personal computing.
The American Farm Bureau, a big farmers' lobby group, is pushing for a simple extension of today's subsidies.
At first "Violent Saturday," the first of Fleischer's many films for 20th Century-Fox, seems like a simple extension of the RKO noirs into widescreen color.
It is that universities are a simple extension of school, and that as at school, students should be given as much attention as possible.
It is not so much a modern version of the Tobin tax, as a simple extension of good old British stamp duty.
The first of these, the gift of shares in private companies, would be a simple extension of allowances already provided for similar gifts of public company shares.
In an interview here, Ms. Maddow described the new deal as more or less a simple extension of her existing one.
The new mayor has been remarkably successful at making it clear that his administration will not be a simple extension of his predecessor's, and the inauguration yesterday continued that theme.
In this paper, first we give a simple extension of a Theorem 1.2 with Aczél's inequality.
Antlers are not true horns; they are a simple extension of bone.
Multivariate linear regression (MLR), another technique, is a simple extension of the well-known univariate case.
More suggestions(15)
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a simple affirmation of
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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