anonymous
  • anonymous
Rationalize the denominator? Please explain every step in some detail. The equation is in the comments below.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\frac{ 3\sqrt{2}-2\sqrt{3} }{ 3\sqrt{2}+2\sqrt{3} }\]
anonymous
  • anonymous
sorry im taking long
anonymous
  • anonymous
1. Multiply the numerator and denominator by the denominator radical. 2. Simplify as needed.

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anonymous
  • anonymous
hopefully that helps :)
anonymous
  • 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
  • anonymous
do you know what a conjugate is?
anonymous
  • anonymous
Yes and the conjugate for the problem is \[3\sqrt{2}-2\sqrt{3}\]
anonymous
  • anonymous
ok so you need to multiply the numerator and denominator by that. Follow the FOIL rules|dw:1435789036541:dw|
anonymous
  • anonymous
Ok so how to I multiply those out it the thing? I just have trouble sometimes with multiplying radicals.
mathstudent55
  • 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
  • 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
  • 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
  • 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
  • anonymous
yes. and you can combine the numerator to get \[\frac{ 30-12\sqrt6 }{ 6 }\]
anonymous
  • anonymous
which is the same as \[\frac{ 30 }{ 6 }-\frac{ 12\sqrt6 }{ 6 }\] and you can reduce fractions
anonymous
  • anonymous
So then we have 5-2√6?
anonymous
  • anonymous
yes
anonymous
  • anonymous
Ok thanks so much this really helped I've been struggling with this for like a week.
anonymous
  • anonymous
you're welcome.

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