The number of values of x satisfying the equation (2x^2-10x)/(x^2-5x)=x-3 is:

1966 AMC 12 Problem 5

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The number of values of

x

satisfying the equation

\frac{2x^2-10x}{x^2-5x}=x-3

is:

zero

one

two

three

an integer greater than

3

Factor numerator and denominator before solving

Do not admit values that make the original denominator zero

The denominator requires

x\ne0

and

x\ne5.

On that domain,

\frac{2x(x-5)}{x(x-5)}=2.

The remaining equation

2=x-3

gives

x=5,

which is excluded. Thus there are no solutions.

Therefore, the correct answer is A.