Question

Express as a fraction with a rational denominator:
5+2√3 / 3+√3
1) 9+√3 over 12 2) 9+√3 over 3 3) 3+√3 over 2 4) 9+√3 over 6

Answer 1

rationalize it :)

Answer 2

You probably mean:\[\frac{ 5+2\sqrt{3} }{ 3+\sqrt{3} }\]The standard trick for this kind of expressions is to multiply both the numerator and the denominator with 3 - √3:\[\frac{ 5+2\sqrt{3} }{ 3+\sqrt{3} }\cdot \frac{ 3-\sqrt{3} }{ 3-\sqrt{3} }\]
Now you have to multiply numerators with each other and also the denominators.
With the denominators, you have the form:\[(a+b)(a-b)=a^2-b^2\]so after multiplying everything, you'll see no more radicals in the denominator!