3. A. Given the equation in terms of $x$
$$
\frac{x}{x-2}+\frac{x-2}{x}=\frac{a-2 x}{x^{2}-2 x}
$$

has exactly one real root. Then the number of real values of $a$ that satisfy this condition is ( ).
(A) 1
(B) 2
(C) 3
(D) 4
3. A. C.

The original equation can be transformed into
$$
2 x^{2}-2 x+4-a=0 \text {. }
$$
(1) When $\Delta=4(2 a-7)=0$, i.e., $a=\frac{7}{2}$, $x=\frac{1}{2}$ satisfies the condition;
(2) When $\Delta=4(2 a-7)>0$, i.e., $a>\frac{7}{2}$, the two distinct real roots of $2 x^{2}-2 x+4-a=0$ must include one extraneous root of the original equation, which can only be 0 or 2. In this case, $a=4$ or 8. After verification, these values satisfy the condition. In summary, there are 3 values of $a$ that meet the conditions.