Answer:
4 - [tex]\sqrt{6}[/tex]
Step-by-step explanation:
Rationalise the denominator by multiplying the numerator and denominator by the conjugate of the denominator.
the conjugate of 4 + [tex]\sqrt{6}[/tex] is 4 - [tex]\sqrt{6}[/tex] , then
= [tex]\frac{10(4-\sqrt{6}) }{(4+\sqrt{6})(4-\sqrt{6}) }[/tex] ← expand denominator using FOIL
= [tex]\frac{40-10\sqrt{6} }{16-6}[/tex]
= [tex]\frac{40-10\sqrt{6} }{10}[/tex] ( divide terms on numerator/ denominator by 10 )
= 4 - [tex]\sqrt{6}[/tex]
