Answer:
A
Step-by-step explanation:
[tex]\frac{10}{9+\sqrt{7} }[/tex]
To rationalise the denominator multiply the numerator and denominator by the conjugate of the denominator.
the conjugate of 9 + [tex]\sqrt{7}[/tex] is 9 - [tex]\sqrt{7}[/tex]
= [tex]\frac{10(9-\sqrt{7}) }{(9+\sqrt{7})(9-\sqrt{7}) }[/tex] ← expand denominator using FOIL
= [tex]\frac{90-10\sqrt{7} }{81-7}[/tex]
= [tex]\frac{90-10\sqrt{7} }{74}[/tex] ( divide terms on numerator/ denominator by 2 )
= [tex]\frac{45-5\sqrt{7} }{37}[/tex] → A
