Given:
There is a fraction given as
[tex]\frac{5}{3+\sqrt{6}}[/tex]
Required:
We need to find the Rationalized denominator
Explanation:
Here we are using below formula to find new denominator
[tex](a+b)(a-b)=a^2-b^2[/tex]
Now
[tex]\frac{5}{3+\sqrt{6}}[/tex]
now to rationalize the the denominator multiply numerator and denominator with
[tex]3-\sqrt{6}[/tex]
applying this
[tex]\frac{5(3-\sqrt{6})}{(3+\sqrt{6)}(3-\sqrt{6)}}[/tex]
now using the formula in denominator
[tex]\frac{15-5\sqrt{6}}{3^2-(\sqrt{6})^2}[/tex]
here we need just denominator
so the denominator is
[tex]3^2-(\sqrt{6})^2=9-6=3[/tex]
Final answer:
New denominator is 3
