Making v/c subject in doppler relativistic equation?

The equation for dopple relativistic motion is


1+z=(1+vcosx/c)/((1-c/v)^0.5) for motion where angle x is 0, after some algebra this becomes 1 + z = [ (1+v/c) / (1-v/c) ]^0.5





my quesiton is how do i make v/c the subject of the equation


thakns everyone.

Making v/c subject in doppler relativistic equation?
If by "subject of the equation" you mean solve for v/c, then set β = v/c, we get:





1 + z = √(1+β)/(1-β)





(1+z)² = (1+β)/(1-β)





(1+z)² (1-β) = (1+β)





(1+z)² - (1+z)²β = 1+β





(1+z)² - 1 = 1+β + (1+z)²β





2z + z² = 1+2β + 2βz + βz²





β = (z² + 2z -1) / (z² + 2z + 2)