Hi everyone, I'm doing Problems Set for revision in section 1D on limits and discontinuity 1D-3 a) (x-2)/(x^2-4) is not simplified for the purpose of finding points of discontinuity; but later on in section 1G Higher Derivatives 1G-1 d) (x^2+5x)/(x+5) in the process of finding y' should be consider x=-5 as a point of removable discontinuity? Thanks!

Question

anonymous · Answer

Problem Set 1

anonymous · Answer

Yes because x = -5 is an asymptote. So when the function reaches -5, it's slope will reach infinite. I hope I understood your question correctly.

anonymous · Answer

Thanks, but I don't think x=-5 is an asymptote: (x^2+5x)/(x+5)=x
What I'd like to know is if there is any rules on when one can simplify an improper fraction.