Answer:
[tex]\frac{20}{13}[/tex] + [tex]\frac{5}{13}[/tex] [tex]\sqrt{3}[/tex]
Step-by-step explanation:
Given
[tex]\frac{5}{4-\sqrt{3} }[/tex]
To rationalise the denominator, multiply the numerator/ denominator by the conjugate of the denominator.
The conjugate of 4 - [tex]\sqrt{3}[/tex] is 4 + [tex]\sqrt{3}[/tex]
= [tex]\frac{5(4+\sqrt{3}) }{(4-\sqrt{3})(4+\sqrt{3}) }[/tex]
= [tex]\frac{20+5\sqrt{3} }{16-3}[/tex]
= [tex]\frac{20+5\sqrt{3} }{13}[/tex]
= [tex]\frac{20}{13}[/tex] + [tex]\frac{5}{13}[/tex] [tex]\sqrt{3}[/tex]
