## LifeIsADangerousGame one year ago I already know the answer, but the way I did it is wrong I think.

$\frac{ \sqrt{x} - 3 }{ 9 - x }$

I multiplied by the conjugate which gave me $\frac{ x - 9 }{ (9 - x)(\sqrt{x} + 3) }$

(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.

4. anonymous

actually that is right

It is? You can multiply the denom by negative one and not the numerator too?

6. 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? $\large - \frac{\cancel{-x + 9}}{(\cancel{-x + 9})(\sqrt{x} + 3)} = -\frac{1}{\sqrt{x} + 3 }$

Oh I see, I think