LifeIsADangerousGame
  • LifeIsADangerousGame
I already know the answer, but the way I did it is wrong I think.
Mathematics
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SOLVED
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katieb
  • katieb
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LifeIsADangerousGame
  • LifeIsADangerousGame
\[\frac{ \sqrt{x} - 3 }{ 9 - x }\]
LifeIsADangerousGame
  • LifeIsADangerousGame
I multiplied by the conjugate which gave me \[\frac{ x - 9 }{ (9 - x)(\sqrt{x} + 3) }\]
LifeIsADangerousGame
  • LifeIsADangerousGame
(the answer is -1/6 btw) I want to cancel out x - 9, but what I did was switch (x - 9) into -9 + x and then multiply the denom by -1, but I don't think that's right.

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anonymous
  • anonymous
actually that is right
LifeIsADangerousGame
  • LifeIsADangerousGame
It is? You can multiply the denom by negative one and not the numerator too?
johnweldon1993
  • johnweldon1993
Well you're not really just multiplying the denominator... \[\large \frac{\sqrt{x} - 3}{9-x} \times \frac{\sqrt{x} + 3}{\sqrt{x} + 3} = \frac{x - 9}{(9 - x)(\sqrt{x} + 3)}\] As you said you can rewrite \(\large (9 - x)\) as \(\large (-x + 9)\) So \[\large \frac{x-9}{(-x + 9)(\sqrt{x} + 3)}\] Now, if you factor out a -1...what do you get? \[\large - \frac{\cancel{-x + 9}}{(\cancel{-x + 9})(\sqrt{x} + 3)} = -\frac{1}{\sqrt{x} + 3 }\]
LifeIsADangerousGame
  • LifeIsADangerousGame
Oh I see, I think
LifeIsADangerousGame
  • LifeIsADangerousGame
Does that look about right? It's an awkward way of showing your work, but it's the only way I can submit it
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