Answer:
StartFraction StartRoot 30 EndRoot minus 3 StartRoot 2 EndRoot + StartRoot 55 EndRoot minus StartRoot 33 EndRoot Over 2
Step-by-step explanation:
Given the surdic equation as shown [tex]\frac{\sqrt{6}+\sqrt{11} }{\sqrt{5}+\sqrt{3} }\\[/tex]
To find the quotient, we will rationalize by multipying both numerator and denominator of the function by the conjugate of the denominator.
Given the denominator [tex]\sqrt{5}+\sqrt{3}[/tex], its conjugate will be [tex]\sqrt{5}-\sqrt{3}[/tex]
Multiplying through by [tex]\sqrt{5}-\sqrt{3}[/tex], we have;
[tex]= \frac{\sqrt{6}+\sqrt{11} }{\sqrt{5}+\sqrt{3} } * \frac{\sqrt{5}-\sqrt{3} }{\sqrt{5}-\sqrt{3} }\\[/tex]
[tex]= \frac{\sqrt{30}- \sqrt{18}+\sqrt{55}-\sqrt{33}}{2}\\= \frac{\sqrt{30}- \sqrt{9*2}+\sqrt{55}-\sqrt{33}}{2}\\= \frac{\sqrt{30}- 3\sqrt{2}+\sqrt{55}-\sqrt{33}}{2}[/tex]
The final expression gives the requires answer
