What is the following quotient? the fraction with numerator 2 and denominator square root of 13 plus square root of 11

Multiply the numerator and denominator by the conjugate, √13 − √11. The denominator becomes (√13 + √11)(√13 − √11) = 13 − 11 = 2, so the quotient is 2(√13 − √11)/2 = √13 − √11. Therefore, the answer is choice C.

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