ALGEBRA: please help me solve this

Directions: Rationalize the denominator and simplify. Show the steps.

3 √2
---------------------
4√3 - √8

HINT: my book says the answer is:

3√6 + 3
----------------
10

I KEEP GETTING THIS ANSWER:

12√6 + 12
-------------------
47

3 √2
---------------------
(4√3 - √8)

3 √2(4√3 + √8)
---------------------
(4√3 - √8)(4√3 + √8)

12√6 + 3√16
---------------------
(48 - 8)


3√6 + 3
----------------
10

(3√2)/[(4√3) - (√8)]

multiply the numerator and denominator by the conjugate of the denominator...

numerator...(3√2) * [(4√3) + √8] = 12√6 + 12

denominator...[(4√3) - √8] * [(4√3) + √8] = 48 - 8 = 40

simplify...common factor of 4 in the numerator and denominator

so,

[(3√6) + 3] / 10

Show your work to learn your mistakes...practice.

(3√2) / (4√3 - √8)

(3√2) (4√3 + √8) / (4√3 - √8)(4√3 + √8)

(3√2) (4√3 + √8) / (16*3 -8)

(3√2) (4√3 + √8) / (48 -8)

(3√2) (4√3 + √8) / 40

[12√(2*3) + 3√(2*8)] / 40

[12√(6) + 3√(16)] / 40

[12√(6) + 3*4] / 40

[4*3√(6) + 4*3] / 40

4[3√(6) + 3] / 40

[3√(6) + 3] / 10

I hope this helps!

4 sqrt 3 - sqrt 8
4 sqrt 3+ sq rt 8
-------------------------
4 sqrt 24 -8
48 -4 sqrt 24
------------------------------------
40

4 sq rt 3+ sqrt 8
3 sq rt 2
---------------------------------
12 sq rt 6 + 3 sq rt 16


12 sqrt 6+12
----------------------
40 take 4 out of the denominator and numerator

3 sqrt 6+3
-----------------
10

the boks answer is correct!

lemme show u;
3 √2 4√3+√8
--------------------- * --------------
4√3 - √8 4√3+√8

12√6+3√16
------------------
40 using a square-b square formula

12√6+ 3*4
---------------
40

12√6+12
-------------
40

12(√6+1) = 3√6 + 3
------------- -------------
40 10

3 √2 4√3 +√8
--------------------- --------------------
4√3 - √8 4√3 - √8

12√6+3√16
---------------------
(4√3)^2 - (√8)^2 since a+b x a-b =a^2-b^2

12√6+3(4)
--------------------
16x3 -8

12√6+12
--------------------
40

taking 4 common
4(3√6+3)
--------------------
40

(3√6+3)
--------------------
10