Question

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

Answer 1

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 \(2\sqrt{6}-1\)

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

having no radicals in the denominator is considered "simpler"

Answer 6

:)

Answer 7

why did you do 1^6?

Answer 8

I meant 1^2

Answer 9

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

Answer 10

you multiplied it by 1, why?