What is the quotient? the fraction with numerator t plus 3 and denominator t plus 4 divided by open paren t squared plus 7 t plus 12 close paren

Factor the quadratic: t² + 7t + 12 = (t + 3)(t + 4). Dividing by this expression means multiplying by its reciprocal, so (t + 3)/(t + 4) × 1/[(t + 3)(t + 4)] simplifies to 1/(t + 4)². The quotient is choice A, one over (t + 4) squared.

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