Respuesta :

luisejr77

Answer:

Last Option

[tex]\sqrt{13} -\sqrt{11}[/tex]

Step-by-step explanation:

To simplify the expression you must multiply the numerator and the denominator of the fraction by the conjugate of the denominator.

If you have an expression of the form

[tex]a +b[/tex] then its conjugate will be [tex]a - b.[/tex]

The result of that multiplication will be

[tex]a ^ 2 -b ^ 2[/tex]

Therefore we have the expression

[tex]\frac{2}{\sqrt{13} +\sqrt{11}}[/tex]

By multiplying by the conjugate of the denominator we have

[tex]\frac{2}{\sqrt{13} +\sqrt{11}}*\frac{\sqrt{13} -\sqrt{11}}{\sqrt{13} -\sqrt{11}}\\\\\\\frac{2(\sqrt{13} -\sqrt{11})}{(\sqrt{13})^2 -(\sqrt{11})^2}\\\\\\\frac{2\sqrt{13} -2\sqrt{11}}{13 -11}\\\\\\\frac{2\sqrt{13} -2\sqrt{11}}{2}[/tex]

[tex]=\sqrt{13} -\sqrt{11}[/tex]

TaeKwonDoIsDead

Answer:

[tex]\sqrt{13}-\sqrt{11}[/tex]

Step-by-step explanation:

When we have an expression in this form:

[tex]\frac{a}{\sqrt{x}+\sqrt{y}  }[/tex]

We need to multiply it by [tex]\frac{\sqrt{x}-\sqrt{y}  }{\sqrt{x}-\sqrt{y}}[/tex]

Let's do this:

[tex]\frac{2}{\sqrt{13}+\sqrt{11}  }*\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}\\=\frac{2(\sqrt{13}-\sqrt{11})}{(\sqrt{13}+\sqrt{11})(\sqrt{13}-\sqrt{11})}\\=\frac{2\sqrt{13} -2\sqrt{11} }{(\sqrt{13} )^2-(\sqrt{11} )^2}\\=\frac{2\sqrt{13} -2\sqrt{11} }{13-11}\\=\frac{2\sqrt{13} -2\sqrt{11} }{2}\\=\frac{2(\sqrt{13} -\sqrt{11} )}{2}\\=\sqrt{13}-\sqrt{11}[/tex]

Note: we used the property  [tex]\sqrt{a} \sqrt{a} =a[/tex]

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