What is √12 + 2 / √12 - 2

Write √12 + 2 / √12 - 2 in the form a+b √3 where a and be are integers.
The answer is 2+√3, but how do you get to this answer?

√12 + 2
**********
√12 - 2

√12 + 2......√12 + 2
**********X**********
√12 - 2.......√12 + 2

12 + 2√12 + 4
****************
......12 - 4

16 + 2√12............√12= √(4*3)= 2 √3
************
......8

16 + 2*(2√3)
**************
.......8

16 + 4√3
**************................Reduce all numbers by 4
.......8

4 + √3
*******.......ANSWER
....2

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Are the parentheses like this?

(√12 + 2) / (√12 - 2)

First factor out √4 from the √12

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

now divide top and bottom by 2

(√3 + 1) / (√3 - 1)

multiply top and bottom by (√3 + 1). This is the conjugate of the bottom, formed by changing the sign

top becomes

(√3 + 1)^2 = 3 + 2√3 + 1 = 4 + 2√3

bottom becomes

(√3 + 1)(√3 - 1) = 3 - 1 = 2

and so forth

You have (√12 + 2)/(√12 - 2), you multiply by the conjugate of the denominator. Given a + √b the conjugate is a - √b, or if you have a - √b the conjugate is a + √b. In your case the conjugate of the denominator is √12 + 2. Multiply (√12 + 2)/(√12 - 2) by (√12 + 2)/(√12 + 2) and get:

(√12 + 2)*(√12 + 2)/(√12 + 2)(√12 - 2) = (16 + 4√12)/8 -----> (16 + 8√3)/8 = 2 + √3