Question

rationalize the denominator:

9 / (7-3sqrt3) - (6-4sqrt3)

Answer 1

ive narrowed the bottom down to either -2, 3+sqrt3, or 4

Answer 2

\(\large\frac{9}{(7-3\sqrt{3}) - (6 - 4\sqrt{3})}\)

Answer 3

yes thats the problem

Answer 4

\(\frac{9}{1+\sqrt{3}}\)

Answer 5

Multiply top and bottom by the expression in the denominator

Answer 6

the top would be 9+9sqrt3?

Answer 7

Yeah

Answer 8

wait

Answer 9

I think you have to multiply top and bottom by the conjugate

Answer 10

that's the only way to get rid of the radical

Answer 11

So muliply top and bottom by \(1 - \sqrt{3}\)

Answer 12

That way, you'll end up with:

\(\frac{9 - 9\sqrt{3}}{1-3}\)

Answer 13

denominator would simplify to -2