what is the following quotient? [tex] \sqrt{6} + \sqrt{11} \div \sqrt{5} + \sqrt{3} [/tex]A. [tex] \sqrt{30} + 3 \sqrt{2} + \sqrt{55} + \sqrt{33} \div 8[/tex]B.[tex] \sqrt{30} - 3 \sqrt{2} + \sqrt{55} - \sqrt{33} \div 2[/tex]C.[tex] \frac{17}{8} [/tex]D.[tex] - \frac {5}{2} [/tex]

Answer:B)  \sqrt{30}  - 3 \sqrt{2}  +  \sqrt{55}  -  \sqrt{33}  \div 2Step-by-step explanation:Step 1: First we have to get rid off the roots in the denominator.To do that, we have to multiply the numerator and the denominator by the conjugate of √5 + √3.The conjugate of √5 + √3 is √5 - √3.Now multiply given expression with √5 - √3(√6 + √11)     (√5 - √3)------------- x   -----------(√5 + √3)        (√5 - √3)Step 2: Multiply the numerators and the denominators.√6√5 - √6√3 +√11√5 -√11√3------------------------------------------(√5)^2 - (√3)^2Now let's simplify to get the answer.√30-√18 +√55 - √33----------------------------- 5 - 3= √30 -3√2 +√55                                     [√18 = √9√2 = 3√2]--------------------------2      The answer is  \sqrt{30}  - 3 \sqrt{2}  +  \sqrt{55}  -  \sqrt{33}  \div 2
Thank you.[tex][/tex]