Solve each formula for the specified variable E/e =R+r/r

Question

E/e = R+r/r

Answer 1

The equation is E/e = (R + r)/r.

The above equation has four different variables E, e, R and r.

Solve for E:

The equation is E/e = (R + r)/r.

Multiply each side by e.

(E/e)e = e[(R + r)/r]

E = e[(R + r)/r]

Solve for e:

The equation is E/e = (R + r)/r.

Apply cross multiplication: If a/b = c/d then ad = bc.

rE = e(R + r)

Divide each side by (R + r).

rE/(R + r) = e(R + r)/(R + r)

rE/(R + r) = e

e = rE/(R + r)

Solve for R:

The equation is E/e = (R + r)/r.

E/e = R/r + 1

Subtract 1 from each side.

E/e - 1 = R/r + 1 - 1

E/e - 1 = R/r

Apply cross multiplication: If a/b = c/d then ad = bc.

r(E/e - 1) = R

R = r(E/e - 1)

Solve for r:

The equation is E/e = (R + r)/r.

E/e = R/r + 1

Subtract 1 from each side.

E/e - 1 = R/r + 1 - 1

E/e - 1 = R/r

Apply cross multiplication: If a/b = c/d then ad = bc.

r(E/e - 1) = R

Divide each side by (E/e - 1).

[r(E/e - 1)] / (E/e - 1) = R/(E/e - 1)

r = R/(E/e - 1)