Answer:
see explanation
Step-by-step explanation:
[tex]\frac{5+2\sqrt{3} }{2+\sqrt{3} }[/tex]
Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator.
the conjugate of 2 + [tex]\sqrt{3}[/tex] is 2 - [tex]\sqrt{3}[/tex] , then
= [tex]\frac{(5+2\sqrt{3})(2-\sqrt{3}) }{(2+\sqrt{3})(2-\sqrt{3}) }[/tex] ← expand numerator/ denominator using FOIL
= [tex]\frac{10-5\sqrt{3}+4\sqrt{3}-6 }{4-2\sqrt{3}+2\sqrt{3}-3 }[/tex]
= [tex]\frac{4-\sqrt{3} }{1}[/tex]
= 4 - [tex]\sqrt{3}[/tex]
