How can I solve this limit algebraically without using the conjugate method?

[daveb]

I can't read the jpeg for some reason, but I also got 3 by decomposing the numerator in the original equation (x^0.5-x^2) = x^0.5(1-(x^0.5)^3) which is a cubic and can be further factored as x^0.5(1-x^0.5)(1+x^0.5+x). The (1-x^0.5) cancel out leaving x^0.5)(1+x^0.5+x). Then take this limit as x goes to 1 gives 3. I imagine that's similar to what wurth did