rationalizing/ is my alg2 correct?

Question

12
------
√7+2

odysey ware says my answers 1√94 is partially right
where did i go wrong


3√6 +5√2
--------------
4√6 -3√2

Answer 1

12/(√7 +2) = 12(√7-2)/(7-4)
=12(√7-2)/3=4(√7 -2)

(3√6 +5√2)/(4√6 -3√2)
= [(3√6 +5√2)(4√6+3√2)]/[(4√6 -3√2)(4√6+3√2)]
=[72+18√3 +40√3+30]/[96 +24√3 -24√3-18]
=(102 +58√3)/78
= (51+29√3)/39

Answer 2

Hi,

12
------
√7+2

Multiply top and bottom by denominator's conjugate, which is the same 2 terms with the opposite sign in between.

12(√7-2)
------------------ =
(√7+2)(√7-2)

12√7-24
------------------------- =
√49+2√7-2√7 - 4

12√7-24
------------ =
7- 4

12√7-24
------------ =
3

Divide every term outside the radical by 3 to reduce.

4√7 - 8 <== answer




3√6 +5√2
--------------
4√6 -3√2

Multiply top and bottom by denominator's conjugate, which is the same 2 terms with the opposite sign in between.

(3√6 +5√2)(4√6 +3√2)
------------------------------- =
(4√6 -3√2)(4√6 +3√2)

12√36 +9√12 + 20√12 +15√4
------------------------------------------- =
16√36 + 12√12 - 12√12 - 9√4

Since √36 = 6. √4 = 2 and √12 simplifies to 2√3, these simplify to:

12(6) +9(2√3) + 20(2√3) +15(2)
------------------------------------------- =
16(6) + 12(2√3) - 12(2√3) - 9(2)

72 + 18√3 + 40√3 + 30
-------------------------------- =
96 + 24√3 - 24√3 - 18

102 + 58√3
----------------
78

Divide everything outside the radical by 2 to reduce them.

51 + 29√3
--------------- <== answer
39

I hope those help!! :-)