Answer:
[tex]v=\frac{2w}{2w-1}[/tex]
Step-by-step explanation:
[tex]w = \frac{v(1-w)}{v-2}[/tex]
Multiply both sides by (v - 2) to remove the fraction
[tex]w(v-2) = v(1-w)[/tex]
Expand both sides
[tex]vw-2w=v-vw[/tex]
Add 2w to both sides (to make the left side simpler)
[tex]vw = v - vw + 2w[/tex]
Subtract (v - vw) from both sides
[tex]vw - (v - vw)=v-vw+2w-(v-vw)[/tex]
Simplify
[tex]2vw - v=2w[/tex]
Factor 2vw - v
[tex]v(2w-1) = 2w[/tex]
Divide both sides by (2w - 1)
[tex]\frac{v\left(2w-1\right)}{2w-1} = \frac{2w}{2w-1}[/tex]
Simplify
[tex]v=\frac{2w}{2w-1}[/tex]
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