I=nE/nr+e for n

Question

solve the formula for the n

Answer 1

Assuming that the equation is I = (nE)/(nr + e),

 

Multiply both sides by nr + e to get:  (nr + e)I = nE

 

Distribute I:  nrI + eI = nE

 

Rearrange terms to get all terms that involve n on one side of the equation and to get all terms that do not involve n on the other side of the equation:

 

nrI - nE = -eI

 

Factor out the common factor, n, on the left side:

 

n(rI - E) = -eI

 

Divide by rI - E:       n = -eI/(rI - E)

 

or equivalently, n = eI/(E - rI)