# How to simplify an expression....

**URL:** <https://community.wolfram.com/t/how-to-simplify-an-expression/3166>\
**Category:** Questions\
**Created:** [September 2, 2014, 7:58pm UTC](https://community.wolfram.com/t/how-to-simplify-an-expression/3166 "2014-09-02T19:58:04Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![jorgerive](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/jorgerive/32/13564_2.png) [@jorgerive](https://community.wolfram.com/u/jorgerive)\
**Post date:** [September 2, 2014, 7:58pm UTC](https://community.wolfram.com/t/how-to-simplify-an-expression/3166/1 "2014-09-02T19:58:04Z")

</div>

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/(s_C_Rf).** 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/(s_C_Rf)** 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

---

<div class="post-metadata">

**Author:** ![mayest](https://avatars.discourse-cdn.com/v4/letter/m/ce73a5/32.png) [@mayest](https://community.wolfram.com/u/mayest)\
**Post date:** [September 2, 2014, 11:25pm UTC](https://community.wolfram.com/t/how-to-simplify-an-expression/3166/2 "2014-09-02T23:25:54Z")

</div>

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.

---

<div class="post-metadata">

**Author:** ![jorgerive](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/jorgerive/32/13564_2.png) [@jorgerive](https://community.wolfram.com/u/jorgerive)\
**Post date:** [September 3, 2014, 12:10pm UTC](https://community.wolfram.com/t/how-to-simplify-an-expression/3166/3 "2014-09-03T12:10:31Z")

</div>

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.