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How to simplify an expression....

Jorge Rivé, CPI
Posted 11 years ago

Hello,

I have an expression: 

vo=(aol id Rf) / (1 + aol + C Rf s).

i define 

beta = 1/(s*C*Rf)

I'd like to simplify the expression by dividing top and bottom by aol, and then substituting beta for 1/(sCRf). I divided the numerator and denominator by aol by separating numerator and denominator using Numerator and Denominator instructions and carrying out the division. However, I'm stuck on how to substitute beta for the expression 1/(sCRf) in the equation.

What I'm ultimately trying to get to is for Mathematica to return:

vo=1/(1+1/(aol*beta))

from the original expression above.

thanks for the help. Jorge
POSTED BY: Jorge Rivé
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Jorge Rivé
Jorge Rivé, CPI
Posted 11 years ago

thanks for the clues....here's what I did based on your input:

In[1233]:= vo = (vo /. sol3[[1]]) // Simplify

Out[1233]= (aol id Rf)/(1 + aol + C Rf s)

In[1234]:= num = Numerator[vo]/aol

Out[1234]= id Rf

In[1235]:= den = Denominator[vo]/aol

Out[1235]= (1 + aol + C Rf s)/aol

In[1243]:= den =   Apart[Expand[den /. {1 + C Rf s -> 1/beta} // Simplify]]

Out[1243]= 1 + 1/(aol beta)

In[1244]:= vo = num/den

Out[1244]= (id Rf)/(1 + 1/(aol beta))

thank you.
POSTED BY: Jorge Rivé

Do you mean this:

 In[1]:= vo = (aol id Rf)/(1 + aol + C Rf s)

  Out[1]= (aol id Rf)/(1 + aol + C Rf s)

  In[2]:= % /. {C Rf s -> beta}

  Out[2]= (aol id Rf)/(1 + aol + beta)

There may be other ways as well, but that gets beta substituted in.
POSTED BY: Tim Mayes
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