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I am trying to understand how to use two verbs in one sentence to explain something. For example, I would like to say that my new idea is based on one idea. Also, it is an extension of the same idea. How to express it correctly in English?

For example,

This new method is based on and an extension of the work of (reference).

I feel that it is not correct to use two verbs in such way? I think that I need to delete one of them? is that correct?

Any help, please?

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    "Based on and an extension of ..." is redundant. By definition, if you extend X from Y, X is based on Y but adds additional features. – Andrew Apr 8 '18 at 12:35
  • @F.AMER Your sentence contains only one verb *is based on. You could easily rewrite it as: *The new method is based on X's work and (further) extends it. – Ronald Sole Apr 8 '18 at 12:36
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So you want to say two things about the method:

  1. It is based on the work.
  2. It is an extension of the work.

To combine these ideas in one sentence you could say:

  1. "This new method is based on and is an extension of the work"
  2. "This new method is both based on and an extension of the work

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