When $x=\frac{1}{5}$, the value of the expression $\frac{x^{2}-4}{x^{2}-2 x}$ is
(A) 0.4
(B) -0.52
(C) -5
(D) 10
(E) 11
Solution 1

We first simplify the expression:

$$
\frac{x^{2}-4}{x^{2}-2 x}=\frac{(x+2)(x-2)}{x(x-2)}=\frac{x+2}{x}=\frac{x}{x}+\frac{2}{x}=1+\frac{2}{x}
$$

(We can cancel the factor of $x-2$ since $x$ is not equal to 2.)

Substituting $x=\frac{1}{5}$, we get $1+\frac{2}{\left(\frac{1}{5}\right)}=1+10=11$.

## Solution 2

Substituting $x=\frac{1}{5}$,

$$
\frac{x^{2}-4}{x^{2}-2 x}=\frac{\frac{1}{25}-4}{\frac{1}{25}-\frac{2}{5}}=\frac{\frac{1}{25}-\frac{100}{25}}{\frac{1}{25}-\frac{10}{25}}=\frac{-\frac{99}{25}}{-\frac{9}{25}}=11
$$

Answer: (E)