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

[Woopa]

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!

 

[Isaac0427]

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.

 

[Woopa]

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.

 

[Isaac0427]

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.

 

[Woopa]

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!