Question

1 divide by
1 + root 5 + root 3

Answer 1

Simplify:

Step-by-step explanation:

$\ Given \ value:\\\\\frac{1}{1+\sqrt{5}+\sqrt{3}} \\\\\ Solution: \\\\\rightarrow \frac{1}{(1+\sqrt{5})+\sqrt{3}} \\\\\rightarrow \frac{1}{(1+\sqrt{5})+\sqrt{3}} \times \frac{((1+\sqrt{5})-\sqrt{3})}{((1+\sqrt{5})-\sqrt{3})} \\\\\rightarrow \frac{((1+\sqrt{5})-\sqrt{3})}{((1+\sqrt{5})^2-(\sqrt{3})^2} \\\\\rightarrow \frac{((1+\sqrt{5})-\sqrt{3})}{((1+5+2\sqrt{5})-(3)} \\\\\rightarrow \frac{((1+\sqrt{5})-\sqrt{3})}{6+2\sqrt{5}-3}$

$\rightarrow \frac{((1+\sqrt{5})-\sqrt{3})}{3+2\sqrt{5}} \\\\\rightarrow \frac{((1+\sqrt{5})-\sqrt{3})}{3+2\sqrt{5}} \times \frac{3-2\sqrt{5}}{3-2\sqrt{5}}\\\\\rightarrow \frac{((1+\sqrt{5})-\sqrt{3})(3-2\sqrt{5})}{(3)^2-(2\sqrt{5})^2}$

$\rightarrow \frac{((1+\sqrt{5})(3-2\sqrt{5}))-(\sqrt{3})(3-2\sqrt{5})}{9- 20} \\\\\rightarrow \frac{3-2\sqrt{5}+3\sqrt{5}-10 -(3\sqrt{3}-2\sqrt{5}\sqrt{3})}{-11} \\\\\rightarrow \frac{3-2\sqrt{5}+3\sqrt{5}-10 -3\sqrt{3}+2\sqrt{5}\sqrt{3}}{-11} \\\\\rightarrow \frac{2\sqrt{5}(\sqrt{3}-1) +3(\sqrt{5}-\sqrt{3}) +7}{-11}$

Learn more:

• Simplify: https://brainly.in/question/9639159