The root(s) of (15)/(x^2-4)-2x-2=1 is (are):

1956 AMC 12 Problem 15

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15.

The root(s) of

\dfrac{15}{x^2-4}-\dfrac2{x-2}=1

is (are):

-5

and

3

\pm2

2

only

-3

and

5

3

only

The original equation requires

x\ne\pm2

Multiply through by

(x-2)(x+2)

and collect terms

For

x\ne\pm2,

multiplying by

x^2-4

gives

15-2(x+2)=x^2-4.

Hence

x^2+2x-15=0,

(x+5)(x-3)=0.

Both

x=-5

and

x=3

satisfy the domain restriction.

Thus, the correct answer is A.