I missed that. I need to edit my post. The 1st problem in the 2nd image is what I am questioning. How did they get -x to become sqrt(x)?That is not the same problem. There is a sign difference in the first term of the numerator.
In the work shown, ##\sqrt{xy} - x## was factored into ##\sqrt x(\sqrt y - \sqrt x)##.I missed that. I need to edit my post. The 1st problem in the 2nd image is what I am questioning. How did they get -x to become sqrt(x)?
Yea that is what's getting me. I get separating sqrt(xy) into sqrt(x)*sqrt(y). I just don't see how the -x turns into sqrt(x) when factoring.In the work shown, ##\sqrt{xy} - x## was factored into ##\sqrt x(\sqrt y - \sqrt x)##.
Oh wait. The -x is technically -x^1 and sqrt of x is technically x^1/2. so if pull a x^1/2 you are left with a x^1/2. Is that correct?In the work shown, ##\sqrt{xy} - x## was factored into ##\sqrt x(\sqrt y - \sqrt x)##.
Clear?
Why over-complicate things?Oh wait. The -x is technically -x^1 and sqrt of x is technically x^1/2. so if pull a x^1/2 you are left with a x^1/2. Is that correct?
But you don't get separating sqrt(xx) into sqrt(x)*sqrt(x)? Edit: or ## \dfrac {x}{\sqrt x} = \sqrt x ##?I get separating sqrt(xy) into sqrt(x)*sqrt(y).
Yes. You could also try multiplying out the factorization @Mark44 showed you and see that you recover what you started with.Oh wait. The -x is technically -x^1 and sqrt of x is technically x^1/2. so if pull a x^1/2 you are left with a x^1/2. Is that correct?