how do i solve 1/R=1/r1+1/r2 solve for r2?

Answer 1

1/r2 = 1/R - 1/r1

r2 = 1 / (1/R -1/r1)

Answer 2

Use your algebra tricks.

Multiply both sides of the equation by the same expression, in this case:

R*r1*r2

Then subtract R*r2 from both sides.

Then use the associative property to separate r2 from r1-R.

Then divide both sides by r1-R, and r2 will be isolated, equivalent to the expression:

(R*r1)/(r1-R)

tada.

The rules of algebra are rules of logic. Just remember you can never unbalance the equivalence, what you do to one side you must do to the other. Keep the goal in mind, separating r2 from everything else.

Answer 3

1/R = 1/r1 + 1/r2
1/r2 = 1/R - 1/r1
r2 = 1/(1/R - 1/r1)

or, more elegantly

r2 = R r1 / (r1 - R)