Can someone show me how this is solved algebraically

1. Oct 8, 2012

chris_0101

1. The problem statement, all variables and given/known data
I need to show how the first equation gives the second equation algebraically

2. Relevant equations

I've tried multiple methods such as rationalizing the denominator with no avail.

3. The attempt at a solution

Any help will be greatly appreciated,

Thanks.

2. Oct 8, 2012

Zondrina

Multiply out the numerator of that mess over c^2. Then find a quick common divisor. Then use the rules :

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

and

$\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{ad}{bc}$

3. Oct 8, 2012

chris_0101

I'm not sure what you mean by "multiply out the numerator of that mess over c^2"?

4. Oct 8, 2012

Zondrina

The quantity $(\frac{u'+v}{1+vu'/c^2})^2$

5. Oct 8, 2012

chris_0101

yea, but how does one multiply out the numerator?
do you mean like this:
(a/b)/c = (a/b)*(1/c)

6. Oct 8, 2012

Zondrina

...

$(\frac{u'+v}{1+vu'/c^2})^2 = (\frac{u'+v}{1+vu'/c^2})(\frac{u'+v}{1+vu'/c^2})$

Now some simple bedmas and you're done....

7. Oct 8, 2012

chris_0101

This is what I got:

(u'^2 + 2u'v + v^2)/((u'^2 v^2)/c^4) + (2((u'v)/c^2) +1

Is this right?