SOLUTION: Simplify {{{4 / (6-(2) sqrt (6))}}}

Question 593848: Simplify
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

First we can reduce the fraction. Factoring a 2 out of both the numerator and denominator we get:

Canceling the factors of 2 we get:

Next we need to rationalize the denominator (i.e. eliminate the square root(s) in the denominator). This denominator has two terms. To rationalize a denominator like this we take advantage of the . Note that the right side of the pattern is made of of perfect square terms! And the left side shows us how to get these perfect square terms. You denominator, , with its subtraction will play the role of (a-b) in the pattern. So get the perfect squares we just need to multiply by (a+b):

Multiplying we get:

which simplifies as follows:

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