The quotient of the given function is [tex]\frac{\sqrt{3}}{2}[/tex]
Given the radical function
Rationalizing the denominator:
[tex]= \dfrac{3\sqrt{8} }{4\sqrt{6} } \times \dfrac{\sqrt{6} }{\sqrt{6} }\\= \dfrac{3\sqrt{8} (\sqrt{6}) }{4\sqrt{6} \cdot \sqrt{6}}\\[/tex]
Multiplying the numerator and denominator:
[tex]=\dfrac{3\sqrt {48}}{4(6)} \\=\dfrac{3(4\sqrt{3})}{24} \\=\dfrac{4\sqrt{3}}{8} \\=\dfrac{\sqrt{3}}{2}[/tex]
Hence the quotient of the given function is [tex]\frac{\sqrt{3}}{2}[/tex]
Learn more on surd function here: https://brainly.com/question/11852465
