Answer:
Answer is [tex]\sqrt{13}-\sqrt{11}[/tex]
Step-by-step explanation:
We need to divide
[tex]\frac{2}{\sqrt{13}+\sqrt{11}}[/tex]
For solving this, we need to multiply and divide the given term with the conjugate of [tex]{\sqrt{13}+\sqrt{11}[/tex]
The conjugate is: [tex]{\sqrt{13}-\sqrt{11}[/tex]
Solving
[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})}\\We\,\, know\,\, that\,\, (a+b)(a-b) = a^2-b^2\\=\frac{2(\sqrt{13}-\sqrt{11})}{(\sqrt{13})^2-(\sqrt{11})^2}\\=\frac{2(\sqrt{13}-\sqrt{11})}{13-11}\\=\frac{2(\sqrt{13}-\sqrt{11})}{2}\\=\sqrt{13}-\sqrt{11}[/tex]
So answer is [tex]\sqrt{13}-\sqrt{11}[/tex]
Answer:
The correct Answer is D[tex]\sqrt{13} - \sqrt{11}[/tex]
Step-by-step explanation:
