Answer:
r = 33 , s = 18
Step-by-step explanation:
Rationalise the denominator by multiplying both numerator and denominator by the conjugate of the denominator.
The conjugate of 4 - [tex]\sqrt{3}[/tex] is 4 + [tex]\sqrt{3}[/tex] , then
[tex]\frac{(6+\sqrt{27})(4+\sqrt{3}) }{(4-\sqrt{3})(4+\sqrt{3}) }[/tex] ← expand numerator/denominator using FOIL
= [tex]\frac{24+6\sqrt{3}+4\sqrt{27}+\sqrt{81} }{16+4\sqrt{3}-4\sqrt{3}-3 }[/tex]
= [tex]\frac{24+6\sqrt{3}+4(3\sqrt{3}+9 }{16-3}[/tex]
= [tex]\frac{33+6\sqrt{3}+12\sqrt{3} }{13}[/tex]
= [tex]\frac{33+18\sqrt{3} }{13}[/tex]
with r = 33 and s = 18
