Respuesta :
You can use the rationalization method in which we multiply the fraction with conjugate of the denominator.
The quotient of the given fraction is given as
[tex]\dfrac{\sqrt{30} + \sqrt{55} - 3\sqrt{2} - \sqrt{33}}{2}[/tex]
How to rationalize a fraction?
Suppose the given fraction is [tex]\dfrac{a}{b + c}[/tex]
Then the conjugate of the denominator is given by b - c
Thus, rationalizing the fraction will give us
[tex]\dfrac{a}{b+c} = \dfrac{a}{b+c} \times \dfrac{b-c}{b-c} = \dfrac{a(b-c)}{b^2 - c^2}\\\\\\(since \: \: (x+y)(x-y) = x^2 - y^2 )[/tex]
We actually rationalize just for the use of that later denominator or numerator(if they seem to be helpful).
Remember that [tex]\dfrac{b-c}{b-c} = 1[/tex] thus, multiplying it with the fraction doesn't change its value, and just change the way how it looks. We assume that b-c is not 0
Using above method for getting the quotient of the given fraction
[tex]\dfrac{\sqrt{6} + \sqrt{11}}{\sqrt{5} + \sqrt{3}} = \dfrac{\sqrt{6} + \sqrt{11}}{\sqrt{5} + \sqrt{3}} \times \dfrac{\sqrt{5} - \sqrt{3}}{\sqrt{5} - \sqrt{3}} = \dfrac{(\sqrt{6} + \sqrt{11}) \times ( \sqrt{5} - \sqrt{3})}{(\sqrt{5})^2 - (\sqrt{3})^2}[/tex]
Simplifying the fraction:
[tex]\dfrac{(\sqrt{6} + \sqrt{11}) \times ( \sqrt{5} - \sqrt{3})}{(\sqrt{5})^2 - (\sqrt{3})^2} = \dfrac{\sqrt{30} + \sqrt{55} - 3\sqrt{2} - \sqrt{33}}{2}[/tex]
Thus,
The quotient of the given fraction is given as
[tex]\dfrac{\sqrt{30} + \sqrt{55} - 3\sqrt{2} - \sqrt{33}}{2}[/tex]
Learn more about rationalizing fractions here:
https://brainly.com/question/14261303
Answer:
B
or
√30-3√2+√55-√33
2
Step-by-step explanation:
on EDGE 2022
