Rationalizing Denominator?

Question

College placement test
3 radical 2 - radical 7
------------------------------- (FRACTION BAR)
4 radical 2 - 3 radical 7
Raltionalize the Denominator THANKS!!!!!!!!!!

Answer 1

(3√2 - √7) (4√2 + 3√7) / (4√2 - 3√7) (4√2 + 3√7)
(24 + 9√14 - 4√14 - 21) / (32 - 63)
(3 + 5√14) / (- 31)
(- 1 / 31) (3 + 5√14)

Answer 2

Multiply the numerator and the denominator by 4sqrt(2) + 3sqrt(7) according to (a + b)(a - b) =
= a^2 - b^2

[3sqrt(2) - sqrt(7)][4sqrt(2) + 3sqrt(7)]
---------------------------------------------------- =
[4sqrt(2) + 3sqrt(7)][4sqrt(2) - 3sqrt(7)]

.... [3sqrt(2) - sqrt(7)][4sqrt(2) + 3sqrt(7)]
= ----------------------------------------------------- =
.... 16*2 - 9*7

= [3sqrt(2) - sqrt(7)][4sqrt(2) + 3sqrt(7)]/(32 - 63) =
= [ 3sqrt(2)*4sqrt(2) + 3sqrt(2)*3sqrt(7) - sqrt(7)*
* 4sqrt(2) - sqrt(7)*3sqrt(7)]/-31 =
= -[12*2 + 9sqrt(14) - 4sqrt(14) - 3*7]/31 =
= -(24 +5sqrt(14) -21)/31 = -[3 + 5sqrt(14)]/31 =
= [-5sqrt(14)-3]/31

Answer 3

3√2 - √7
-----------
4√2 - 3√7


multiply both top and bottom by the conjagate of 4√2 - 3√7, which is 4√2 + 3√7

3√2 - √7 ........ 4√2 + 3√7
-------------- x ------------------
4√2 - 3√7 ...... 4√2 + 3√7


distribue
24 + 9√14 - 4√14 - 21
----------------------------
.... 32 - 63

simplify
5√14 + 3
--------------
... -31

or (-5√14 - 3)/31