What is the following quotient? the fraction with numerator 9 plus square root of 2 and denominator 4 minus square root of 7

Multiply the numerator and denominator by the conjugate, 4 + √7, to remove the radical from the denominator. The denominator becomes 4² − (√7)² = 16 − 7 = 9, and the numerator becomes 36 + 9√7 + 4√2 + √14. This matches choice C.

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