Respuesta :
Function assigns one element of one set to the other specific element of another set. The quotient of the fraction [tex]\dfrac{2}{\sqrt{13}+\sqrt{11}}[/tex] is [tex]{\sqrt{13}-\sqrt{11}}[/tex].
What is a Function?
A function assigns the value of each element of one set to the other specific element of another set.
As the fraction is given to us,
[tex]\dfrac{2}{\sqrt{13}+\sqrt{11}}[/tex]
Rationalizing the fraction we will get,
[tex]=\dfrac{2}{\sqrt{13}+\sqrt{11}} \times \dfrac{{\sqrt{13}-\sqrt{11}}}{{\sqrt{13}-\sqrt{11}}}\\\\= \dfrac{2({\sqrt{13}-\sqrt{11}})}{(\sqrt{13})^2-(\sqrt{11})^2}\\\\= \dfrac{2({\sqrt{13}-\sqrt{11}})}{13-11}\\\\=\dfrac{2({\sqrt{13}-\sqrt{11}})}{2}[/tex]
Now, if we divide the numerator by the denominator to get the quotient we will get,
[tex]= \dfrac{2({\sqrt{13}-\sqrt{11}})}{2}\\\\={2({\sqrt{13}-\sqrt{11}})}\div 2\\\\={\sqrt{13}-\sqrt{11}}[/tex]
Hence, the quotient of the fraction [tex]\dfrac{2}{\sqrt{13}+\sqrt{11}}[/tex] is [tex]{\sqrt{13}-\sqrt{11}}[/tex].
Learn more about Function:
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The quotient of the given number start Fraction 2 over start root 13 end root start root 11 end root end Fraction.
[tex]\sqrt{13}-\sqrt{11}[/tex]
What is the quotient?
Quotient is the resultant number which is obtained by dividing a number with another. Let a number a is divided by number b. Then the quotient of these two number will be,
[tex]q=\dfrac{a}{b}[/tex]
Here, (a, b) are the real numbers.
The number Start Fraction 2 Over Start Root 13 End Root Start Root 11 End Root End Fraction given can be written as,
[tex]\dfrac{2}{\sqrt{13}+\sqrt{11}}[/tex]
Let the quotient of this division is n. Therefore,
[tex]n=\dfrac{2}{\sqrt{13}+\sqrt{11}}[/tex]
By rationalizing the denominator, we get,
[tex]n=\dfrac{2}{\sqrt{13}+\sqrt{11}}\times\dfrac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}\\n=\dfrac{2(\sqrt{13}-\sqrt{11})}{(\sqrt{13})^2-(\sqrt{11})^2}\\n=\dfrac{2(\sqrt{13}-\sqrt{11})}{13-11}\\\\n=\dfrac{2(\sqrt{13}-\sqrt{11})}{2}\\n=\sqrt{13}-\sqrt{11}[/tex]
Hence, the quotient of the given number start Fraction 2 Over Start Root 13 End Root Start Root 11 End Root End Fraction.
[tex]\sqrt{13}-\sqrt{11}[/tex]
Learn more about the quotient here;
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