limits and continuity

[kc_math]

Hi! I am doing an online calculus course, I got this problem from the link(screenshot)

https://www.dropbox.com/s/qzswcfb125wl45t/calculus limits.png?dl=0


I don't understand where the expression [FONT=MathJax_Main]−[FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]28[/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]96[/FONT][/FONT] from the denominator comes from. This is professor's solution, not mine, but I don't understand how he gets
that [FONT=MathJax_Main]−[FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]28[/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]96[/FONT][/FONT] and what happens to it later (the underlined expressions). Also, for some reason, while I was taking a screenshot the fractional lines in some parts disappeared, this is not the mistake of the one who posted the solution. I don't question the solution, just want to understand it.

Thanks!

 

[Deleted member 4993]

Hi! I am doing an online calculus course, I got this problem:View attachment 4778
I don't understand where the expression fronm the denominator comes from. This is professor's solution, not mine, but I don't understand how he gets
that [FONT=MathJax_Main]−[FONT=MathJax_Main]2[/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]2[/FONT][FONT=MathJax_Main]+[/FONT][FONT=MathJax_Main]28[/FONT][FONT=MathJax_Math]x[/FONT][FONT=MathJax_Main]−[/FONT][FONT=MathJax_Main]96[/FONT][/FONT] and what happens to it later8 (the underlined expressions). Thanks!

The image for some reason omitted fractional lines in some parts, but I hope you can see it (it's not an error on part of the solution)

That is a mistake - replace -2x² + 28x - 96 by (x-8)

I suppose that expression is a random-child of copy/paste marriage. Otherwise, the calculation seems to be correct.

 

[kc_math]

You mean that -2x² + 28x - 96 should't be there at all, have no relation whatsoever with the example? Because he braks it apart and cancells it further down.