Question

1/s+1/r=1/b. solve for b?

rational expressions

Answer 1

`b = (rs) / (r + s)`

Explanation:

Given

`(1)/(s) + (1)/(r) = (1)/(b)`

Solve for `b`

1) Get `b` out of the denominator by multiplying all the terms on both sides by `b` and letting the denominator cancel.
After you have multiplied and canceled, you will have this:
`(b)/(s) + (b)/(r) = (1)/(1)`

2) Clear the first fraction by multiplying all the terms on both sides by `s` and letting that denominator cancel.
`(b)/(1) + (bs)/(r) = (s)/(1)`

3) Clear the second fraction by multiplying all the terms on both sides by `r` and letting that denominator cancel.
`(br)/(1) + (bs)/(1) = (rs)/(1)`

This is the same as
`br + bs = rs`

4) Factor out `b`
`b(r + s) = rs`

5) Divide both sides by `(r + s)` to isolate `b`
`b = (rs) / (r + s)` `larr` answer

Answer:
`b = (rs) / (r + s)`