Simplify: (x² - 16) / (x + 4)

Question

Accepted Answer

x - 4. The numerator x² - 16 is a difference of squares, which factors as (x + 4)(x - 4). So the expression becomes (x + 4)(x - 4) / (x + 4). The common factor (x + 4) cancels, leaving x - 4 (with the restriction that x ≠ -4 since the original expression is undefined there).

The result x + 4 would come from incorrectly canceling and keeping the wrong factor; after canceling (x + 4) from numerator and denominator, the remaining factor is (x - 4), not (x + 4). The result x² - 4 might come from subtracting only the constant (16 - 4 = 12... this doesn't match) or from incomplete factoring. The result x - 16 might come from incorrectly attempting to "cancel" the +4 by subtracting it from the constant -16, which is not valid algebraic simplification.

Simplifying rational expressions is a key skill for the DSST exam. Students must be able to factor both numerators and denominators, identify common factors, and cancel them properly. The difference of squares pattern a² - b² = (a + b)(a - b) is one of the most frequently used factoring techniques.

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