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.
To solve the equation S = a/(1-r) for r, follow these steps:
1. Multiply both sides of the equation by 1-r to eliminate the denominator on the right side: S * (1 - r) = a
2. Distribute the S on the left side of the equation: S - S * r = a
3. Subtract S from both sides to isolate the term with r: -S * r = a - S
4. Multiply both sides by -1 to make the coefficient of r positive: r = (-a + S) / S
Therefore, the solution to the equation S = a/(1-r) for r is r = (-a + S) / S.