13) Given the equalities on the left, which of the statements on the right is true?
(I) $\frac{x^{3}-5 x^{2}}{x^{2}}=\frac{3 x-15}{3}$,
(II) $\frac{x-5}{1 / 2}=\frac{3 x-15}{3 / 2}$,

(A) (I), (II), and (III) are true for every real $x$

(B) (I), (II), and (III) are false for every real $x$

(III) $\frac{x-5}{2}=x-\frac{5}{2}$

(C) for every real $x$, if (II) is true, then (III) is also true

(D) for every real $x$, if (II) is true, then (I) is also true

(E) for every real $x$, if (I) is true, then (III) is false.
13) The answer is $(\mathbf{E})$. (I) is false only for $x=0$, because the denominator becomes zero and cannot be simplified. (II) is obviously always true. (III) is true only for $x=0$, as seen by solving the first-degree equation. Therefore, only answer (E) is acceptable.