I am having trouble getting from step 1 to step 2. here are 2 examples. This is in reference to relativity of simultaneity

[can't_think_of_a_name]

The rules I try to apply in no order and different combos are switching the denominator and numerator on both sides of the equation. Also if I remove a variable I do what I do to one side as the other side of the equation. Cross multiplying and factoring out a variable. I can't seem to get the answers. Any help is appreciated?  

 

 

 

Edited June 2, 2020 by can't_think_of_a_name

[Endy0816]

Sorry, your image didn't upload correctly. Might try uploading on imgur if the forums are causing the issue.

[can't_think_of_a_name]

Also picture 1 is not step 1 Picture 2 is not step 2. Picture 1 I need to get to step 1 to step 2 same with picture 2

[Endy0816]

For the second did you try multiplying by 1 = (c+v)/(c+v) and 1 = (c-v)/(c-v) respectively to simplify(Difference of two squares)?

Keep in mind: 1 - (v²/c²) = (c² - v²)/ c²

Edited June 3, 2020 by Endy0816

[can't_think_of_a_name]

How is 1 - (v²/c²) = (c² - v²)/ c²   the same?

 

 

[Strange]

1 hour ago, can't_think_of_a_name said:

How is 1 - (v²/c²) = (c² - v²)/ c²   the same?

(c² - v²) / c²

Dividing through by c²:

c²/c² - v²/c²

Simplifying:

1 - v²/c²

Does that make sense?

[can't_think_of_a_name]

Yep perfectly clear now thank.

The part that confuses me  in the first picture is I have 2 T_A  on two different side of the equation and don't know how to get rid of either. Any advice?
Any advice in general when doing this type of question? I remember hearing if I had a^2 I wanted a^2 because the units match. I don't have a^2 just using that as an example.

Edited June 6, 2020 by can't_think_of_a_name

[can't_think_of_a_name]

I think I got the first picture. But tips would appreciated what kind of math is this called ? I assume some form of algebra?

[joigus]

On 6/7/2020 at 2:19 AM, can't_think_of_a_name said:

I think I got the first picture. But tips would appreciated what kind of math is this called ? I assume some form of algebra?

It's the algebra of real numbers. It's not "some form" of special algebra.

If you can point to what the problem is with @Strange's explanation:

On 6/6/2020 at 10:17 AM, Strange said:

(c² - v²) / c²

Dividing through by c²:

c²/c² - v²/c²

Simplifying:

1 - v²/c²

Does that make sense?

Maybe I can try to make it simpler. But I think you should really go over the steps. It's really all down to multiplication and division of real numbers.

[Strange]

On 6/7/2020 at 12:33 AM, can't_think_of_a_name said:

The part that confuses me  in the first picture is I have 2 T_A  on two different side of the equation and don't know how to get rid of either. Any advice?

I'll show you the first few steps. See if you can go from there:

[math](T_a)_{rear} = \frac {\frac{L_a}{2} - v(T_a)_{rear} }{c}[/math]

Divide the RHS through by c

[math](T_a)_{rear} = \frac{L_a}{2c} - \frac {v}{c}(T_a)_{rear} [/math]

Take Ta to the other side:

[math](T_a)_{rear} +  \frac {v}{c}(T_a)_{rear} = \frac{L_a}{2c}[/math]

 

Can you see the way from there? (Hint: you can create a [math](1 +  \frac {v}{c})[/math] on the LHS)

General advice? Practice lots of basic algebra problems!

 

[can't_think_of_a_name]

I think I got the correct answer I will double check later.

Where can I find questions that can be solved that are similar to the ones I posted?


Also I have another question hopefully the picture is attached. How does La/v etc become Lb/v etc?  I start  with the information L_moving because Alice is moving. I don't have Bob's frame. My point is I have L_moving not L_stationary. I am  referencing to this formula L' = L/y. In order to get L shouldn't I go  L = L'Y?

 

 

 

 

Edited June 9, 2020 by can't_think_of_a_name