(1/r)=(a/a+b) solve for b

Question

i don't know how to even start to solve for b. how do i get the b by itself?

Answer 1

Esteban,

 

The easiest way to understand this is to clear the denominators by multiplying both sides of the equation by each in turn.  Such multiplication doesn't change the equality.

 

Starting with:  (1/r) = a/(a + b), first multiply both sides by (a + b)

(1/r)(a + b) = [a/(a + b)](a + b) = a  since (a + b)/(a + b) = 1 , now multiply by the r

r(1/r)(a + b) = ra

(a + b) = ra

b = ra -a = a(r - 1)