What is the algebra concept used to derive time dilation formula?

AI Thread Summary
The discussion centers on deriving the time dilation formula and the algebraic steps involved in the process. A user seeks clarification on the transition between two lines of their working, specifically regarding the algebraic concept used. The response highlights the importance of correctly applying division to all terms in an equation, emphasizing that division distributes across addition and subtraction. The user acknowledges the explanation and expresses gratitude for the clarification. Understanding these algebraic principles is crucial for accurately deriving the time dilation formula.
Woopa
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Homework Statement
Time dilation derivation
Relevant Equations
Pythagoras theorem
Hi this is my first post the forum, nice to meet you all.

I am trying to derive the time dilation formula following the image attached. However I am unsure of the algebra being used toget from the 2nd line of working to the 3rd line. Can someone please tell me what the name of the algebra concept being used is and some resources I can use to understand it.

Thank you!
 

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Woopa said:
Homework Statement:: Time dilation derivation
Relevant Equations:: Pythagoras theorem

Hi this is my first post the forum, nice to meet you all.

I am trying to derive the time dilation formula following the image attached. However I am unsure of the algebra being used toget from the 2nd line of working to the 3rd line. Can someone please tell me what the name of the algebra concept being used is and some resources I can use to understand it.

Thank you!
It's just doing two steps at once. First divide both sides by c2, and then factor out a t2 from the left hand side. I don't know if the "[]" brackets are confusing you, but if so they mean the same thing at parenthesis.
 
Isaac0427 said:
It's just doing two steps at once. First divide both sides by c2, and then factor out a t2 from the left hand side. I don't know if the "[]" brackets are confusing you, but if so they mean the same thing at parenthesis.

Thanks for replying Isaac.

I'm definitely doing something wrong. Here is my working below.
 

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Woopa said:
Thanks for replying Isaac.

I'm definitely doing something wrong. Here is my working below.
Ah. Be careful when you divide by c2; you have to divide ALL terms (including v2t2). After dividing by c2 you should get t2 - v2t2/c2 = t02.

I tutor math physics, and this is perhaps the most frequent algebra mistake I see. Division distributes to addition/subtraction. You just have to be careful when you divide a sum or difference by something to make sure you are dividing every term.
 
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Isaac0427 said:
Ah. Be careful when you divide by c2; you have to divide ALL terms (including v2t2). After dividing by c2 you should get t2 - v2t2/c2 = t02.

I tutor math physics, and this is perhaps the most frequent algebra mistake I see. Division distributes to addition/subtraction. You just have to be careful when you divide a sum or difference by something to make sure you are dividing every term.
Got it! Thanks Isaac, beautiful explanation!
 
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