The discussion revolves around understanding the factoring methods used in solving multivariable limits, specifically focusing on the manipulation of expressions involving square roots and variables. Participants are examining how terms in the numerator of a function are transformed during the factoring process.
The conversation is ongoing, with participants exploring different interpretations of the factoring process. Some have offered insights into the mathematical properties of square roots and exponents, while others are seeking further clarification on specific steps in the manipulation of the expressions.
There is an emphasis on ensuring that variables x and y are non-negative for the discussed manipulations to be valid. Participants are also noting discrepancies in the original problem setup, which may affect the understanding of the factoring process.
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)?FactChecker said: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)##.quittingthecult said: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.Mark44 said: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?Mark44 said:In the work shown, ##\sqrt{xy} - x## was factored into ##\sqrt x(\sqrt y - \sqrt x)##.
Clear?
Why over-complicate things?quittingthecult said: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 ##?quittingthecult said: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.quittingthecult said: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?