Quick question, say I'm simplying a solution I got using the quadratic equation and I run into this:

Original version (as posted by OP):

x = -7 +- 3 sqrt(5) over 3

Edited version: $$x = \frac{-7\pm 3 \sqrt{5} }{3}$$ Would the two $3$s cross each out leaving the answer to be $x = -7 \pm \sqrt{5}$, or is that illegal in terms of rules and you have to simplify all the terms, including the $-7$ if you were to simplify correctly.

Thanks!

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$\frac{a\pm b}{3} = \frac a 3 \pm \frac b 3$ –  lhf Dec 6 '11 at 11:58
Does my eq. edit correspond to what you wanted to ask? –  user13838 Dec 6 '11 at 12:20
@percusse: your edit makes Gerry's first sentence (and indeed the whole answer) look rather silly. Please do not edit in such ambiguous cases but rather suggest your interpretation in a comment. –  t.b. Dec 6 '11 at 12:23
@t.b. It says quadratic equation so it doesn't take too much to guess what OP means, that's why I asked him (it doesn't take too much effort to rollback anyway). And I don't think any edit can make Gerry's arguments silly. –  user13838 Dec 6 '11 at 12:27
@percusse: Unfortunately you've removed the opportunity for us to impress on OP the importance of parentheses... –  Ｊ. Ｍ. Dec 6 '11 at 12:29

I'm a little late on the scene, but from your most recent comments you still haven't seen the light. Maybe this will help.

$$\frac{-7\pm 3 \sqrt{5} }{3} \;\; =\;\; \left(\frac{1}{3}\right) \left(\frac{-7\pm 3 \sqrt{5}}{1}\right) \;\;= \;\; \left(\frac{1}{3}\right)\left(-7 \; \pm \; 3 \sqrt{5}\right)$$

$$= \;\; \left(\frac{1}{3}\right)(-7) \; \pm \; \left(\frac{1}{3}\right)\left(3 \sqrt{5}\right) \;\; = \;\; \left(\frac{1}{3}\right)\left(\frac{-7}{1}\right) \; \pm \; \left(\frac{1}{3}\right)\left(\frac{3 \sqrt{5}}{1}\right) \;\; = \;\; -\frac{7}{3}\; \pm \; \frac{3 \sqrt{5}}{3}$$

Usually people do all this in one step (see the first comment under your question, the comment by lhf) and write:

$$\frac{-7\pm 3 \sqrt{5} }{3} \;\; = \;\; -\frac{7}{3}\; \pm \; \frac{3 \sqrt{5}}{3}$$

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People usually do a little bit more, simplifying to $$-{7\over3}\pm\sqrt5$$ but I think what you've done should be most helpful to OP. –  Gerry Myerson Dec 7 '11 at 3:44
What you have written is ambiguous. You might mean $x=-7+(3\sqrt5/3)$, but I bet you mean $x=(-7+3\sqrt5)/3$. So let me ask you: in $(1+2)/2$, can you "cancel the 2s" to get $(1+2)/2=(1+1)/1=2/1=2$?
The trouble with leaving out the parentheses is that only you would know whether $1+2/2$ means $(1+2)/2$ or $1+(2/2)$. Everyone else would have to guess which one you meant. That's why we use parentheses; we don't want to make people guess what we mean. With $1+(2/2)$, sure, you can cancel. –  Gerry Myerson Dec 6 '11 at 12:15