I already know the answer, but the way I did it is wrong I think.

Question

lifeisadangerousgame · Answer

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

lifeisadangerousgame · Answer

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

lifeisadangerousgame · Answer

(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.

anonymous · Answer

actually that is right

lifeisadangerousgame · Answer

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

johnweldon1993 · Answer

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 · Answer

Oh I see, I think

lifeisadangerousgame · Answer

Does that look about right? It's an awkward way of showing your work, but it's the only way I can submit it