What is the following quotient? the fraction with numerator square root of 6 plus square root of 11 and denominator square root of 5 plus square root of 3

Multiply the numerator and denominator by the denominator’s conjugate, √5 − √3. The denominator becomes (√5 + √3)(√5 − √3) = 5 − 3 = 2. The numerator expands to √30 − √18 + √55 − √33, and √18 = 3√2, giving (√30 − 3√2 + √55 − √33)/2. This is choice A.

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