Solve for a. c=(ab) / (a+b)

`c=(ab)/(a+b)` solve for
a

first multiply both sides by (a+b) to get rid of
fraction

`c(a+b)=ab`

Now
distribute

`ac+bc=ab`

Now we
want to get all the terms with a as a factor on one side and everything else on the
other

`ac-ab=-bc`

now factor
out the a

`a(c-b)=-bc`

Now
divide by
`c-b`

`a=-(bc)/(c-b)`

And we
can get rid of the negative sign by noting
`(c-b)=-(b-c)`

To get our final answer `a =
(bc)/(b-c)`