Algebra

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Solve S=a/(1-r) for r

S = a/(1-r)
Multiply both sides by 1-r
S*(1-r) = [(1-r)*a]/(1-r)
Simplify
S*(1-r) = a
Multiply terms on the left.
S - S*r = a
Subtract S from both sides.
S-S*r - S = a - S
Simplify
-S*r = a - S
Multiply both sides by -1
S*r = -a+S
Divide both sides by S
S*r/S = (-a + S)/S
r = (S-a)/S
Check my work carefully.

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