Make u the subject of the formula: (would be helpful if steps are included) ( a)/(1 - u) = (b)/(1 + u) ​

Question

Make u the subject of the formula:

(would be helpful if steps are included)

`( a)/(1 - u) = (b)/(1 + u)`
​

Answer 1

u =
`(b-a)/(a+b)`

Explanation:

Given

`(a)/(1-u)` =
`(b)/(1+u)` ( cross- multiply )

a(1 + u) = b(1 - u) ← distribute parenthesis on both sides

a + au = b - bu ( add bu to both sides )

a + au + bu = b ( subtract a from both sides )

au + bu = b - a ← factor out u from each term on left side

u(a + b) = b - a ← divide both sides by (a + b)

u =
`(b-a)/(a+b)`