Rearranging equation - Relativistic doppler

[roberto85]

Homework Statement

The hydra cluster is 900 Mpc (3x10^9 light years) away. Calcium atoms emit a spectral line of wavelength 396.8 nm. This line is observed at 487.5 nm. The velocity of the cluster, v, is given by ($$\lambda$$ =c/f)

487.5 = 396.8 SQRT((1+v/c)/(1-v/c))

How do i find v please?

Homework Equations

The Attempt at a Solution

I need to rearrange and this example says take v/c to one side and solve but i don't know how. Well i have taken the numbers to one side, squared them and left with (1+v/c)/(1-v/c) on the other side, how do i find v? Thanks

 

[Mark44]

1. Divide both sides by 396.8.
2. Square both sides.
3. Multiply both sides by (1 - v/c).
4. Carry out the multiplication on the left side.
5. Get all terms involving v on one side.
6. Factor v out.
7. Divide both sides by the coefficient of v.

That should pretty much do it

 

[roberto85]

Thanks :)