# Thread: Can I simplify this more?

1. ## Can I simplify this more?

$\frac{3-\sqrt{5}(2cos\theta )}{3-\sqrt{5}(cos\theta )}$

2. ## Re: Can I simplify this more?

Originally Posted by amthomasjr
$\frac{3-\sqrt{5}(2cos\theta )}{3-\sqrt{5}(cos\theta )}$
Do you consider $1-\frac{\sqrt{5}\cos(\theta)}{3-\sqrt{5}\cos(\theta)}$ more simplified? Otherwise, I don't think so.

3. ## Re: Can I simplify this more?

Originally Posted by amthomasjr
$\frac{3-\sqrt{5}(2cos\theta )}{3-\sqrt{5}(cos\theta )}$

Before the age of calculators or computer algebra systems we wanted students to "rationalize".
It made approximations easier and more actuate.
But that is no longer an issue.

But you must defer to your instructor on this matter.

4. ## Re: Can I simplify this more?

Originally Posted by Plato

Before the age of calculators or computer algebra systems we wanted students to "rationalize".
It made approximations easier and more actuate.
But that is no longer an issue.

But you must defer to your instructor on this matter.
It is an issue of whether you want your fraction to make sense. All surds can be written as finite lengths, and it makes sense to divide a finite length into a countable number of pieces. It does not however make sense to divide any length into an uncountable number of pieces.

5. ## Re: Can I simplify this more?

Originally Posted by Prove It
It does not however make sense to divide any length into an uncountable number of pieces.
So what do we do with $\frac{2}{\pi}~?$

6. ## Re: Can I simplify this more?

generally speaking we avoid irrational numbers in the denominator. We get rid of these irrational by multiplying and dividing be the rationalizing factor of the denominator, which in this case is ( 3 + Sqr root 5 cos theta)

7. ## Re: Can I simplify this more?

Originally Posted by Plato
So what do we do with $\frac{2}{\pi}~?$
I realise there's no way to simplify a transcendental denominator. It's all a question of elegance. The whole purpose of simplifying is to make things make as much sense as possible where possible.