Question

Express v in terms of w

Answer 1

`v=(2w)/(2w-1)`

Explanation:

`w = (v(1-w))/(v-2)`

Multiply both sides by (v - 2) to remove the fraction

`w(v-2) = v(1-w)`

Expand both sides

`vw-2w=v-vw`

Add 2w to both sides (to make the left side simpler)

`vw = v - vw + 2w`

Subtract (v - vw) from both sides

`vw - (v - vw)=v-vw+2w-(v-vw)`

Simplify

`2vw - v=2w`

Factor 2vw - v

`v(2w-1) = 2w`

Divide both sides by (2w - 1)

`(v\left(2w-1\right))/(2w-1) = (2w)/(2w-1)`

Simplify

`v=(2w)/(2w-1)`

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