Which solution to the equation the fraction with numerator 3 and denominator A plus 2 plus 2 over A is equal to the fraction with numerator 4 A minus 4 and denominator A squared minus 4 is extraneous?

Multiply both sides by A(A + 2)(A − 2), the common denominator, to get 3A(A − 2) + 2(A + 2)(A − 2) = A(4A − 4). Simplifying gives A² − 2A − 8 = 0, which factors as (A − 4)(A + 2) = 0, so the candidate solutions are A = 4 and A = −2. But A = −2 makes a denominator zero in the original equation, so it is extraneous; the correct choice is A equals negative 2.

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