SOLUTION: Rationalize the denominator and simplify. All variables represent positive real numbers. square root 11 / square root 33

SOLUTION: Rationalize the denominator and simplify. All variables represent positive real numbers. square root 11 / square root 33 - square root 5

Question 423052: Rationalize the denominator and simplify. All variables represent positive real numbers. square root 11 / square root 33 - square root 5
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Rationalizing a two-term denominator takes advantage of the pattern:

Notice that the left side is a product of two-term expressions, like your denominator. And the result, the right side, is made up of nothing but perfect squares.

Your denominator has a "-" between the two terms. SO it will play the role fo (a-b) with the "a" being and the "b" being . To get the prefect squares, we need to multiply the (a-b) by (a+b). And if we multiply the denominator by something we must also multiply the numerator by the same thing. So we will multiply the numerator and denominator by (a+b), i.e. :

We use the distributive Property to multiply the numerators. In the denominators we know how it will multiply because of the pattern we're using:

which simplifies as follows:

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