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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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    Can you show me how the final answer would look then? Thanks.2011-12-06

2 Answers 2

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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.2011-12-07
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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 $(1+2)/2=(1+1)/1=2/1=2$?

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    At this point, I think I refer you to Dave Renfro's answer. Leave a comment if there are still questions to clear up.2011-12-07