Given that a = b/(1+b) , express b in terms of a. a = (b)/(1 + b) ​

Question

Given that a = b/(1+b) , express b in terms of a.

`a = (b)/(1 + b)`
​

Answer 1

b = -
`(a)/(a-1)`

Explanation:

a =
`(b)/(1+b)` ( multiply both sides by 1 + b to clear the fraction )

a(1 + b) = b ← distribute parenthesis on left side

a + ab = b ( subtract b from both sides )

a + ab - b = 0 ( subtract a from both sides )

ab - b = - a ← factor out b from each term on left side

b(a - 1) = - a ( divide both sides by a - 1 )

b = -
`(a)/(a-1)`