Inequalities with Rational Functions (Precalculus - College Algebra 47)

How to determine the interval of the solution set for inequalities with rational functions. Focus will be on using multiplicity of x-intercepts and vertical asymptotes to determine the truth of intervals of the x-axis.

[HunterNapier]

Cannot thank you enough for these, you have given me hope I can actually pass PreCalc. My teacher could really use several novels out of your library of skills, because they seriously do not explain ANYTHING. I'd been afraid of math and trying for higher education in the STEM field because of people like that, and it is such a relief to see that I'm not stupid and I can understand if someone takes the time to actually explain it.

[nathanfitzgerald]

I'm hurting for linear algebra right now, my first math class without you and its been painful

[Cometastraea]

Prof Leonard- I am taking Diff Eq this quarter online and your videos are catching me up to speed. Thank you so much for everything you do. You've really carried me through calculus and beyond.

[deji_ace]

Passed online calc thanks to this superman right here. Came to see if you're doing alright and Thank God you are!

[georgesadler]

Professor Leonard, thank you for explaining and solving Inequalities with Rational Functions. Solving the examples in different ways should be helpful to all students in Precalculus, College Algebra and Calculus.

Thank you so much for these videos Prof Leonard. Your hard work and knowledge helps a lot of people.

[jassimjaved]

Thank you so much Professor Leonard, you are the best math teacher ever! I am glad that you are sharing your knowledge with us. I am very grateful for it!

[maryhowell]

Thank you thank you thank you! this helps so much!

[anynomouse]

I hope you are doing well professor leonard !

[rossenpetrov]

46:10 - the horizontal asymptote should be at y=1 (not y=3) because the rational inequality is not in 'normalized' form (<=0).
Otherwise, great lecture (as always)!

[HenryThe]

Hey Professor, I had a question that you may have touched on before

So I've been graphing the functions after figuring out the inequalities just to see what the final products are, and I remember that you can find simplified versions of the functions without the vertical asymptotes and whatnot by just actually doing the long division (For example, with the equations starting at 27:38, if you simplified it, you'd get x^2-2x+2, or the parabola that matches over the original function).

I was trying to do this with the last equation in the video and I came across an issue, I couldn't get a simplified version without it still being in fraction form. Is this normal for functions with an end behavior of 1/x or did I do something wrong? I was trying to do the long division and ended up getting something weird like (2/x+1/2x...), I've never divided in reverse like that before.

[jonasmduduzibhuda]

Thank you so much Prof. Kindly advice as to whether you do have any videos( or any site that you can recommend) on ANOVA and any experiment designs lectures?

[tommasotiberi]

Wanna see where a function is greater or equal than another?
Go look where their difference is greater or equal than zero



Gotta love math ❤

[somasahu]

U didn't mention wavy curve method?!?

[veryhealthy]

Hey, can anyone else check for the solution to the ex given at 36:31? I am actually getting something completely different and even on Desmos, im getting:

(-inf, -1) U (-1, 0] U (1, 2)

Edit: Its ok, turns out I got the 'right' answer but misinterpreted f(x) >= 0

[أ.أحمدكاملالزهيري]

You need put camera more near whiteboard because we see you from mobile

[TheSpasmer]

You still haven't covered trigonometry. This is crazy