Respuesta :
When one number is divided by the other number, then the result obtained is known as the quotient of two numbers.
The resultant quotient is [tex]\dfrac{1-\sqrt{2} }{4\sqrt{3} }[/tex].
What is quotient?
When one number is divided by the other number, then the result obtained is known as the quotient of two numbers.
Given information-
The fraction number given in the problem is,
[tex]=\dfrac{2-\sqrt{8} }{4\sqrt{12} }[/tex]
To simplify the which are under the root, brake them in simple multiplication number as,
[tex]\dfrac{2-\sqrt{8} }{4\sqrt{12} }=\dfrac{2-\sqrt{2\times2\times2} }{4\sqrt{2\times2\times3} }[/tex]
Take out numbers from root which are makes pairs (as pair number make perfect square). Thus,
[tex]\dfrac{2-\sqrt{8} }{4\sqrt{12} }=\dfrac{2-2\sqrt{2} }{4\times2\sqrt{3} }[/tex]
Take the common number out,
[tex]\dfrac{2-\sqrt{8} }{4\sqrt{12} }=\dfrac{2(1-\sqrt{2} )}{4\times2\sqrt{3} }\\\dfrac{2-\sqrt{8} }{4\sqrt{12} }=\dfrac{1-\sqrt{2} }{4\sqrt{3} }[/tex]
Thus the resultant quotient is [tex]\dfrac{1-\sqrt{2} }{4\sqrt{3} }[/tex].
Learn more about division of fraction number here;
https://brainly.com/question/1622425
