The complete set of x -values satisfying the inequality (x^2-4)/(x^2-1)>0 is the set of all x such that:

(E) x is any real number except 1 or -1

1969 AMC 12 Problem 14

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14.

The complete set of

x

-values satisfying the inequality

\dfrac{x^2-4}{x^2-1}\gt0

is the set of all

x

such that:

x\gt2

x\lt-2

-1\lt x\lt1

x\gt2

x\lt-2

x\gt1

x\lt-2

x\gt1

x\lt-1

x

is any real number except

1

-1

The sign can change only at

-2,

-1,

1,

and

2

Test one point in each interval and exclude zeros and undefined points

Factor the expression as

\frac{(x-2)(x+2)}{(x-1)(x+1)}.

A sign chart at

-2,

-1,

1,

and

2

shows it is positive on

(-\infty,-2)\cup(-1,1)\cup(2,\infty).

The endpoints

\pm2

give zero and

\pm1

are undefined.

Therefore, the correct answer is A.