## anonymous one year ago Rationalize the denominator? Please explain every step in some detail. The equation is in the comments below.

1. anonymous

$\frac{ 3\sqrt{2}-2\sqrt{3} }{ 3\sqrt{2}+2\sqrt{3} }$

2. anonymous

sorry im taking long

3. anonymous

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

4. anonymous

hopefully that helps :)

5. 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.

6. anonymous

do you know what a conjugate is?

7. anonymous

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

8. anonymous

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

9. anonymous

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

10. 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.

11. 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.

12. 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

13. 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 $\frac{ 18-6\sqrt{6}-6\sqrt{6}+12 }{ 6 }$

14. anonymous

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

15. anonymous

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

16. anonymous

So then we have 5-2√6?

17. anonymous

yes

18. anonymous

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

19. anonymous

you're welcome.