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If I have

$$ 60 = 40/X + X $$

How do I remove $40$ and find $X$?

As I understand it, I have to multiply both sides by $X$. But if I do that then I'm left with

$$ \begin{eqnarray*} &60X = 40 + X &\Rightarrow \\ &60X - X = 40 &\Rightarrow \\ &X - X = 40 / 60 &\Rightarrow \\ & 1 = 2/3 & \end{eqnarray*} $$

And I think I ended at the wrong spot...

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    Minor slip. When you multiply both sides by $X$, you should end up with $60X=40+X^2$. You may have forgotten to multiply the $X$ at the right end by $X$.2011-10-17
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    @Andre Nicolas - Do I have to do that to all other variables in the equation? for instance if that equation was instead `60 = 40 / X + x^2 + X` it would come out to be `60X = 40 + X^3 + x^2`?2011-10-17
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    @Aedon, yes -- you do it for each _term_, whether or not they contain variables. It's not a special magical rule, it's just the ordinary $a(b+c)=ab+ac$ applied with $a=x$, $b=\frac{40}{x}$ and $c=x$.2011-10-17

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You know $X\ne 0$ so you can multiply by it. That will leave you a quadratic equation for $X$.

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    I'm not sure I follow, how will that leave me with a quadratic equation for X?2011-10-17
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    Multiplying both sides by $X$ gives $60X=40+X^2\implies X^2-60X+40=0$.2011-10-17
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    Ok I see now, thank for the help :)2011-10-17