Solve for S P=S-Sdt

$P = S - S d t$

Rewrite the equation as $S - S d t = P$ .

$S - S d t = P$

Factor $S$ out of $S - S d t$ .

Factor $S$ out of $S^{1}$ .

$S \cdot 1 - S d t = P$

Factor $S$ out of $- S d t$ .

$S \cdot 1 + S (- 1 d t) = P$

Factor $S$ out of $S \cdot 1 + S (- 1 d t)$ .

$S (1 - 1 d t) = P$

Rewrite $- 1 d$ as $- d$ .

$S (1 - d t) = P$

Divide each term in $S (1 - d t) = P$ by $1 - d t$ and simplify.

Divide each term in $S (1 - d t) = P$ by $1 - d t$ .

$\frac{S (1 - d t)}{1 - d t} = \frac{P}{1 - d t}$

Simplify the left side.

Cancel the common factor of $1 - d t$ .

Cancel the common factor.

$\frac{S (1 - d t)}{1 - d t} = \frac{P}{1 - d t}$

Divide $S$ by $1$ .

$S = \frac{P}{1 - d t}$