Question

Rationalize the denominator of \[9/(7-3\sqrt{3}) - ( 6-4\sqrt{3})\]

Answer 1

is it\[9 \over (7-3\sqrt3)-(6-4\sqrt3)\]?

Answer 2

is that the question I mean

Answer 3

yes.

Answer 4

ok let's just look at the denominator:\[7-3\sqrt3-6+4\sqrt3=1+\sqrt3\]so now our problem is\[9\over1+\sqrt3\]multiply top and bottom by 1-sqrt3:\[{9(1-\sqrt3)\over(1+\sqrt3)(1-\sqrt3)}={9-9\sqrt3\over 1-3}={9-9\sqrt3\over-2}=(-9/2)(\sqrt3-1)\]

Answer 5

thanks! :)

Answer 6

we do medals here, not thx, but you're welcome :)