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

rational expressions

1 Answer
Nov 24, 2017

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)