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Any mathematicians out there?

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I am currently reading ‘Why Does E=MC2?’ By Brian Cox and Jeff Foreshaw, and an excellent book it is too. However, in the chapter on Special Relativity, it shows how the Lorenz Transformation, which expresses how time as seen by two observers differs when one of them is moving, and the other is stationary, can be derived simply.

At one stage (page 48), they produce an expression to describe the ratio between the rate at which time passes for the moving observer and the rate for the stationary one, which is:

c/√(c^2-v^2 )

They then say, and I quote: “which can be written, with a little more mathematical rearranging, as:”

1/√(1-v^2/c^2 )

Now, I have described the context in which these expressions have been used, but I do not believe that this is required to help me with my problem, which is, what “mathematical rearranging” has been performed to get from the first expression to the second?

Although I consider myself reasonably good at maths, I just cannot see how its been done, and its driving me mental !!

Either I am missing something very simple, or the rearranging they refer to is not so simple, and they have dodged the issue for the sake of simplicity in the book. Help!

Just for clarity, I have put the two expressions into a .PDF file, which is attached.


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Divide top & bottom by c. The top goes to 1 straight away.

1/c * sqrt (c^2 - v^2) is the same as 1 * sqrt(1/c^2 * (c^2 - v^2)) ; the 1 * can of course be removed & expanding the multiplcation inside the square root sign yields the wanted result directly.

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