Answer:
30 + 12[tex]\sqrt{5}[/tex]
Step-by-step explanation:
To rationalise the denominator, multiply the numerator and denominator by the conjugate of the denominator.
The conjugate of 2[tex]\sqrt{5}[/tex] - 4 is 2[tex]\sqrt{5}[/tex] + 4 , then
[tex]\frac{12\sqrt{5}(2\sqrt{5}+4) }{(2\sqrt{5}-4)(2\sqrt{5}+4) }[/tex] ← expand denominator using FOIL
= [tex]\frac{120+48\sqrt{5} }{20-16}[/tex]
= [tex]\frac{120+48\sqrt{5} }{4}[/tex] ( divide each term on numerator by 4 )
= 30 + 12[tex]\sqrt{5}[/tex]
