# Thread: To simplify or not to simplify...

1. ## To simplify or not to simplify...

For this question, rather than simplifying the R^2 and the R^3, they just move the R^2 over and times by 0, etc.
I'm wondering, why not simplify? They simplified to a degree before hand, so why not now? How do you know when to stop? They get the right answer of course, but how do I know when to simplify and when not to?

2. As far as I can see there is no simplification.. A fraction is zero only when the numerator is 0. They have just used that idea.

I am not sure what you refer to as simplification, tell us where you want to do it and how? Then we can comment on it.

3. Originally Posted by Naur
For this question, rather than simplifying the R^2 and the R^3, they just move the R^2 over and times by 0, etc.
I'm wondering, why not simplify? They simplified to a degree before hand, so why not now? How do you know when to stop? They get the right answer of course, but how do I know when to simplify and when not to?
The aim is to solve the problem at hand, here it is to find $\displaystyle R$. To do this one follows the easiest route, in this case that is multiplying both sides by $\displaystyle R^2$

RonL

4. However there is nothing wrong with
$\displaystyle \frac{4 \pi r^3 - 100}{r^2} = 0$

$\displaystyle 4 \pi r - \frac{100}{r^2} = 0$

$\displaystyle 4 \pi r = \frac{100}{r^2}$

$\displaystyle 4 \pi r^3 = 100$

etc.

This method simply includes two extra lines of work, however.

-Dan

5. I was under the impression that the $\displaystyle {r^3} / {r^2}$ could cancel down to $\displaystyle {r^1}$

6. Originally Posted by Naur
I was under the impression that the $\displaystyle {r^3} / {r^2}$ could cancel down to $\displaystyle {r^1}$
Yes it does on line 2, but you end up multiplying by $\displaystyle r^2$ again on line 4 of topsquark's post.

RonL

7. Oh hey you're right.
I also though that the $\displaystyle {r^2}$ on the bottom would cancel out completely. But of course, it wouldn't. I knew that.
Thanks very much to all of you.