What is the solution to the equation the fraction with numerator 1 and denominator h minus 5 plus the fraction with numerator 2 and denominator h plus 5 is equal to the fraction with numerator 16 and denominator h squared minus 25 ?

The denominators require h ≠ 5 and h ≠ −5. Since h² − 25 = (h − 5)(h + 5), combine the left side over that common denominator: [1/(h − 5)] + [2/(h + 5)] = (h + 5 + 2h − 10)/(h² − 25) = (3h − 5)/(h² − 25). Equating numerators gives 3h − 5 = 16, so h = 7. This is allowed, so the solution is choice C, h is equal to 7.

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