Which inequality is equivalent to the fraction with numerator x minus 6 and denominator x plus 5 is greater than or equal to the fraction with numerator x plus 7 and denominator x plus 3 ?

Subtract the right-hand fraction from the left, keeping the common denominator (x + 5)(x + 3). The numerator becomes (x − 6)(x + 3) − (x + 7)(x + 5) = (x² − 3x − 18) − (x² + 12x + 35) = −15x − 53. The denominator is x² + 8x + 15, so the equivalent inequality is (−15x − 53)/(x² + 8x + 15) ≥ 0, which is choice D.

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