2.119 The number of values of $x$ that satisfy the equation $\frac{2 x^{2}-10 x}{x^{2}-5 x}=x-3$ is
(A) 0.
(B) 1.
(C) 2.
(D) 3.
(E) An integer greater than 3.
(17th American High School Mathematics Examination, 1966)
[Solution] From $x^{2}-5 x=x(x-5)$, when $x \neq 0,5$, the equation can be simplified to $2=x-3$, which means $x=5$, contradicting the previous assumption.
Therefore, this equation has no solution.
Hence, the correct choice is $(A)$.