How to find one expression in terms of another expression?

• To: mathgroup at smc.vnet.net
• Subject: [mg119735] How to find one expression in terms of another expression?
• From: Jacare Omoplata <walkeystalkey at gmail.com>
• Date: Sun, 19 Jun 2011 19:29:04 -0400 (EDT)

```I want to find dT in terms of dt. They are given below.

In[1]:= Element[{x1, x2, t1, t2, u, c}, Reals]

Out[1]= (x1 | x2 | t1 | t2 | u | c) \[Element] Reals

In[3]:= T1 = (t1 - ((u x1)/c^2))/Sqrt[1 - (u^2/c^2)]

Out[3]= (t1 - (u x1)/c^2)/Sqrt[1 - u^2/c^2]

In[4]:= T2 = (t2 - ((u x2)/c^2))/Sqrt[1 - (u^2/c^2)]

Out[4]= (t2 - (u x2)/c^2)/Sqrt[1 - u^2/c^2]

In[5]:= dT = T2 - T1

Out[5]= -((t1 - (u x1)/c^2)/Sqrt[1 - u^2/c^2]) + (
t2 - (u x2)/c^2)/Sqrt[1 - u^2/c^2]

In[6]:= dt = t2 - t1

Out[6]= -t1 + t2

If I knew that dT can be written in terms of dt in the form,
dT = a dt + b,
Can I use Mathematica to find a and b?

I tried using  Solve[dT == a dt + b, dt], but that gives an error.

If I didn't know that dT can be expressed this way, can I still
express it in terms of dt ?

```

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