@John Fredsted

Thank you for your reply, and for telling me a simple and very helpful code.

@John Fredsted 

Hello, by the way, as this is a good opportunity I think I will ask you.
How do you manage so called session dependency?
Do you think that only sort command remove that dependency?
Thinking of it, it might be better to avoid to use commands related to op, but
doing so surely makes it inconvenient to write codes.
I hope for hearing from you about your dealing with those dependencies in general.

@acer 
Thank you.
I spent a time in understanding your code. And, now, I understand it.

And, the actual numerator and the actual denominator are different from those seen in screen, multiplied by , in my case, Omega, and sometimes multiplied by (-1), so that in that case the signs of the denominater and the numelator have changed.

And, the order of terms in the same expression differs at each time restart is executed and
the calculation begins from the top of the worksheet.

Your code is about the way to deal without these complexities.
Extracting contents of an expression as you do in your code
is very useful information to me.

Thank you.

p.s.
I surely understand your code. But, what I think I had understood haven't
fallen into my mind,yet. So, there might be the case that I have to ask to you
about your code. In that case, I will be very glad if you rely to my then question.

@John Fredsted 

Thank you very much.
expand in expand(x/denom(a)) was what I couldn't write before I asked about the question.
I owe you a lot.
 

I think that some example in a worksheet might be helpful
to those who would answer your question.

@John Fredsted 

Thank you.
The problem I had was resolved owing to you.
 

Please write what you want to do more in detail.

@Carl Love 

Thank you.
Now, I understand well how map is used.
Thank you for giving me an example of using map.

@tomleslie

[1/x, y, z] has list in op(0,[1/x,y,z]). So, what I thought at first was that changing that list to `*` would change

[1/x,y,z] to (1/x)*y*z. But it didn't. So, I used  op as op([1/x,y,z]). Then, the output I wrote at the biginning of this thread appeared, so I asked about it.

@Joe Riel 

Thank you for your answer.

I could understand well, and my problem was solved owing to you.

@awass 

At Preferences->Open and Save, I think you can see radio buttons of Smart brabra.

Taking off the check at  Smart quotes radio button might resolve your problem.

@tomleslie 

Thank you for your teaching me. 
Your code with freeze and thaw helped a lot to me.
 

@Kitonum 

Thank you for your teaching me.

I could understand your code, and it worked well.

Thank you.

Addition:

Thank you for reminding me of the use of evalindets.

@Carl Love 

What you write is quite right. 
On the other hand, the idea of "Office Hour" looked very interesting to me,
because where I live, there are no such things for classes.

At the time it will be opened, I will be sleeping because of the time difference of 12 hours 
between US and Japan. So, I think I will not attend it.

 

@acer

Thank you for your relpy.
I want the output to be shown as 

And, I have an additional question. I attached another file, diff_3.

diff_3.mw

, where I changed g(t,y) to y/t  at "i" expression.

Then, the outcome of diff becomes

But, I want this to be shown as 

or , where the latter is more desiable than the former.