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- anonymous

Rationalize the denominator? Please explain every step in some detail. The equation is in the comments below.

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- anonymous

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- anonymous

\[\frac{ 3\sqrt{2}-2\sqrt{3} }{ 3\sqrt{2}+2\sqrt{3} }\]

- anonymous

sorry im taking long

- anonymous

1. Multiply the numerator and denominator by the denominator radical.
2. Simplify as needed.

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- anonymous

hopefully that helps :)

- anonymous

No it didn't really help I need a step by step walk through I already knew that is what I needed to do I just don't really know how.

- anonymous

do you know what a conjugate is?

- anonymous

Yes and the conjugate for the problem is \[3\sqrt{2}-2\sqrt{3}\]

- anonymous

ok so you need to multiply the numerator and denominator by that. Follow the FOIL rules|dw:1435789036541:dw|

- anonymous

Ok so how to I multiply those out it the thing? I just have trouble sometimes with multiplying radicals.

- mathstudent55

You can use FOIL twice, or you can use the square of a binomial in the numerator, and the product of a sum and a difference in the denominator to save time.

- anonymous

Multiply the numbers outside the radical, and multiply the ones under the radical.
For example let's take the numerator
(3√2)(3√2) = 9√4 = 9(2) = 18
(3√2)(-2√3) = -6√6
(-2√3)(3√2) = -6√6
(-2√3)(-2√3) = 4√9 = 4(3) = 12
Combine them all to get the numerator. Try it with the denominator. And yes definitely use the shortcut above once you understand where it comes from.

- freckles

\[\frac{a-b}{a+b} \\ =\frac{a-b}{a+b} \cdot \frac{a-b}{a-b} \\ = \frac{a^2-2ab+b^2}{a^2-b^2 }\]
juut applying the formulas mentioned by @mathstudent55

- anonymous

Ok so @peachpi the numerator is \[18-6\sqrt{6}-6\sqrt{6}+12\] so to get the denominator we need to do this
(3√2)(3√2) = 9√4 = 18
(3√2)(-2√3) = -6√6
(2√3)(3√2) = 6√6
(2√3)(-2√3) = -4√9 = -12
which means the denominator is just 6 which makes the equation \[\frac{ 18-6\sqrt{6}-6\sqrt{6}+12 }{ 6 }\]

- anonymous

yes. and you can combine the numerator to get
\[\frac{ 30-12\sqrt6 }{ 6 }\]

- anonymous

which is the same as
\[\frac{ 30 }{ 6 }-\frac{ 12\sqrt6 }{ 6 }\]
and you can reduce fractions

- anonymous

So then we have 5-2√6?

- anonymous

yes

- anonymous

Ok thanks so much this really helped I've been struggling with this for like a week.

- anonymous

you're welcome.

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