Simplify the rational expression: (2x^2 - 8)/(x^2 - 4), x ≠ ±2

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Multiple Choice

Simplify the rational expression: (2x^2 - 8)/(x^2 - 4), x ≠ ±2

Explanation:
Factoring reveals the simplification clearly. The numerator 2x^2 - 8 factors as 2(x^2 - 4) = 2(x-2)(x+2). The denominator x^2 - 4 factors as (x-2)(x+2). So the fraction becomes [2(x-2)(x+2)] / [(x-2)(x+2)]. For x not equal to ±2, the common factor (x-2)(x+2) cancels, leaving 2. Therefore the simplified expression is 2 (with the understanding that x ≠ ±2 due to the original denominator).

Factoring reveals the simplification clearly. The numerator 2x^2 - 8 factors as 2(x^2 - 4) = 2(x-2)(x+2). The denominator x^2 - 4 factors as (x-2)(x+2). So the fraction becomes [2(x-2)(x+2)] / [(x-2)(x+2)]. For x not equal to ±2, the common factor (x-2)(x+2) cancels, leaving 2. Therefore the simplified expression is 2 (with the understanding that x ≠ ±2 due to the original denominator).

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