Answer:
13+7√3
Step-by-step explanation:
The denominator will be rational when it is multiplied by the opposite ± expression, called the conjugate.
[tex]\frac{5 + \sqrt{3}}{2-\sqrt{3}}[/tex]
[tex]= \frac{5 + \sqrt{3}} {2-\sqrt{3}} X \frac{2+\sqrt{3}}{2+\sqrt{3}}[/tex] Multiplying by 1 does not change the number. (It equals 1 because the numerator and denominator are the same).
[tex]= \frac{(5 + \sqrt{3})(2+\sqrt{3})} {(2-\sqrt{3})(2+\sqrt{3})}}[/tex]
[tex]= \frac{10 + 5\sqrt{3} + 2\sqrt{3}+3 }{4 - 2\sqrt{3}+ 2\sqrt{3}-3}[/tex] Distribute over brackets
[tex]= \frac{13 + 7\sqrt{3} }{4 -3}[/tex] Combine like terms
[tex]= \frac{13 + 7\sqrt{3} }{1}[/tex]
[tex]= 13 + 7\sqrt{3}[/tex]
