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symbolic algebra and substitution

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I'm trying to simplify 5 equations by substituting until I have one equation and just a few inputs.  The symbolic result is extremely complex and could easily be simplified but no matter what I try, I can't get it to simplify or collect on terms.  Further, when I later use the derived equation, the numerical value is incorrect.  It is challenging to find where the error is occurring.

 

Suggestions?

thanks


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