Subtract the Following Two Equations and Solve For $S$ $\begin{gathered}S=a+a x+a x^{2}+a x^{3}+\cdots+a x^{12} \\X S=a x+a x^{2}+a x^{3}+a x^{4}+\cdots+a x^{13}\end{gathered}$

Multiple Choice

Subtract the following two equations and solve for $S$ :
$\begin{gathered}S=a+a x+a x^{2}+a x^{3}+\cdots+a x^{12} \\X S=a x+a x^{2}+a x^{3}+a x^{4}+\cdots+a x^{13}\end{gathered}$
Assume $x$ is not equal to 1 .

A) $S=\frac{a\left(1-x^{13}\right) }{x}$
B) $S=\frac{a\left(1-x^{13}\right) }{1-x}$
C) $S=-a\left(1-x^{13}\right)$
D) $S=a\left(1-x^{13}\right)$