Einstein velocity addition solving for v

[gtguhoij]

Homework Statement

I am trying to solve for v in the equation below. I just want to confirm I got the correct answer. Can someone confirm? If my writing is to messy I will type it. Just let me know if you can read it?

Relevant Equations

$w = \frac {u+v} {uv+1}$

 

[BvU]

If my writing is to messy

It is.

 

[gtguhoij]

$w = \frac {u+v} {uv+1} =$
$\frac {w} {u+v} = \frac {1} {uv+1} =$
$\frac {w} {u} = \frac {1} {(uv+1) -v} =$
$\frac {w} {u} = \frac {1} {(-uv^2-v)} =$
$\frac {w} {u} = \frac {1} {(-uv^2-v)} =$
$\frac {vw} {u} = \frac {v} {(-uv^2-v)} =$
$\frac {vw} {u} = \frac {-v} {(-uv^2-v)} =$
$\frac {vw} {u} = \frac {-v} {(-uv^2-v)}$
$\frac {uvw} {u} = \frac {-vu} {(-uv^2-v)}$
$\frac {uvw} {u} = \frac {-v} {(-v^2-v)} =$
$\frac {uvw} {u} = \frac {-v} {(-v^2-v)} =$
$\frac {u} {uvw}= \frac {(-v^2-v)} {-v} =$
$\frac {u} {uvw-v}= {(-v^2-v)} =$
$\frac {-vu} {uvw}= \frac {-v} {(-v^2-v)} =$
$\frac {-u} {uw}= \frac {1} {(v+1)} =$
$\frac {-u} {uw-1}= \frac {1} {(v)} =$
$\frac {-u} {uw-1}= \frac {1} {(v)} =$ $\frac {uw+1} {u} = {(v)}$

Is there any way to use latex outside the physics forum?

 

[PeroK]

Are you trying to solve for $v$ in terms of $u$ and $w$? Quicker is:
$$\frac{u + v}{1 + uv} = w \ \Rightarrow \ u + v = w + uvw \ \Rightarrow \ v(1 -uw) = w - u \ \Rightarrow \ v = \frac{w - u}{1 - uw}$$

 

[BvU]

Is there any way to use latex outside the physics forum?

It's more or less the standard for scientific writing

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