## anonymous 4 years ago How do I simplify 2√6 / 2√6 + 1? The answer is 24 - 2√6 / 23?.. How? D:

1. asnaseer

use the identity:$a^2-b^2=(a+b)(a-b)$to remove the radical expression in the denominator. so, in this case, multiply numerator and denominator by $$2\sqrt{6}-1$$

2. anonymous

that's what I did but should I be multiply 2 x 2 cand √6 x √6?

3. asnaseer

$\frac{2\sqrt{6}}{2\sqrt{6}+1}=\frac{2\sqrt{6}}{2\sqrt{6}+1}*\frac{2\sqrt{6}-1}{2\sqrt{6}-1}=\frac{2\sqrt{6}(2\sqrt{6}-1)}{(2\sqrt{6}+1)(2\sqrt{6}-1)}$$=\frac{(2*\sqrt{6}*2*\sqrt{6}-2\sqrt{6})}{(2\sqrt{6})^2-1^2}=\frac{4*6-2\sqrt{6}}{4*6-1}=\frac{24-2\sqrt{6}}{23}$

4. anonymous

Although, I don't understand why the exercise is called "simplify". There is nothing simple about the alternate form.

5. asnaseer

having no radicals in the denominator is considered "simpler"

6. anonymous

:)

7. anonymous

why did you do 1^6?

8. anonymous

I meant 1^2

9. asnaseer

$a(b+c)=ab+ac$so:$2\sqrt{6}(2\sqrt{6}-1)=(2\sqrt{6})*(2\sqrt{6})-(2\sqrt{6})*1$$=2*2*\sqrt{6}*\sqrt{6}-2\sqrt{6}=4*6-2\sqrt{6}=24-2\sqrt{6}$

10. anonymous

you multiplied it by 1, why?

11. asnaseer

|dw:1327863505800:dw|

12. anonymous

ohh, so it's not -2√6?

13. asnaseer

it is - look at what I typed up there, you do get $$-2\sqrt{6}$$ when you multiply $$2\sqrt{6}$$ by -1.

14. asnaseer

I guess I used:$a(b-c)=ab-ac$in this case.

15. anonymous

ohh.. sorry :(

16. asnaseer

do you understand the process now?

17. anonymous

yes, I do thank you!

18. asnaseer

yw