1. Rationalize Denominator & Simplify

(24√3+27)/(2√3+3)

(24√3+27)/(2√3+3)*
(2√3-3)/(2√3-3)

Numerator:

(24√3+27)(2√3-3) becomes

9(7 - 2√3)

Denominator:

(2√3+3)(2√3-3) becomes 3.

We now have 9(7 - 2√3)/3, which further simplifies to 3(7 - 2√3).

Correct?

Ok.

4. Re: Rationalize Denominator & Simplify

Solved incorrectly. Try again

5. Re: Rationalize Denominator & Simplify Originally Posted by mak29 Solved incorrectly. Try again
Thanks for letting me know.

6. Re: Rationalize Denominator & Simplify

computer says

$\frac{24\sqrt{3}+27}{2\sqrt{3}+3}=21-6 \sqrt{3}$

7. Re: Rationalize Denominator & Simplify Originally Posted by mak29 Solved incorrectly. Try again
WHY? His solution is 3(7 - 2sqrt(3)) which is correct...

8. Re: Rationalize Denominator & Simplify Originally Posted by DenisB WHY? His solution is 3(7 - 2sqrt(3)) which is correct...
So, I am correct. Why try again?

9. Re: Rationalize Denominator & Simplify Originally Posted by mak29 Solved incorrectly. Try again
I'm so sorry .

You have solved it correctly.

10. Re: Rationalize Denominator & Simplify Originally Posted by mak29 I'm so sorry .

You have solved it correctly.
Not a problem.

11. Re: Rationalize Denominator & Simplify Originally Posted by harpazo (24√3+27)/(2√3+3)
To:harpazo, do you not think that $\dfrac{(24\sqrt3+27)}{(2\sqrt3+3)}$ is not easier to read than what you posted?
All you need do is a basic bit of LaTeX "\dfrac{(24\sqrt3+27)}{(2\sqrt3+3)}" rapped in dollar signs.
Learning LaTeX is so easy. Very few commands will make your posts so much more readable and inviting.
Why not try?

12. Re: Rationalize Denominator & Simplify

I rather use MathMagic Lite.

13. Re: Rationalize Denominator & Simplify Originally Posted by harpazo I rather use MathMagic Lite.
What is MathMagic?

14. Re: Rationalize Denominator & Simplify Originally Posted by Plato What is MathMagic?
MathMagic Lite is a free app that allows you to express math in LaTex fashion without the technicality of dealing with the slash bar, dollar sign, brackets, colon, semicolon, etc.