Advanced Functions 5.5 Solving Rational Inequalities

Using graphing, number lines or interval tables we can solve rational inequalities. Be sure not to simply cross multiply for these equations or you may be eliminating some of your solution.

[@reading-_____-5299]

Thank you for the wonderful videos! I have one question, for number (5f) shown in the video, how did you know that the function would not cross the HA for sections 1 and 3? (I usually plug in a large value for x to find out, but is there a quicker method?) Thank you for your time!

[@mshavrotscanadianuniversit6234]

Your method is good. Another way to tell would be to set the equation equal to the value of the HA and see if there is a solution.

[@reading-_____-5299]

@@mshavrotscanadianuniversit6234 Thank you so much!

[@tinted8244]

this video REALLY helped me, thank you so much, My final exam is tomorrow :)

[@mshavrotscanadianuniversit6234]

Good luck! Hope you will take calculus and vectors next semester!

[@tinted8244]

@@mshavrotscanadianuniversit6234 Thank you so much, I think the exam went well! I have calc and vectors next year, but I intend of binge watching all your calc videos right now. Thank you so much for what you do!

[@gheedwattar2612]

Hi Ms.Havrot, if we are asked to solve an inequality then graph it, do we have to draw ONLY the values under zero?

[@mshavrotscanadianuniversit6234]

I'm afraid you need to be more specific. If you are being asked to show where the function is less than zero I would still draw the entire function and show where it is less than zero with a dotted line or a colored pencil (making sure not to include the points on the x axis). If you are asked to show the solution on a number line that would also be different. Still open circles on the places where the function has a height of zero.

[@gheedwattar2612]

@@mshavrotscanadianuniversit6234 that clarified my question, thank you!

[@ShivayshKumar]

Hello Ms.Havrot! Thanks for uploading these, as preparing for grade 12 has been incredibly swift as they are so organized and detailed! I just had a question about the first example you showed us in this video. Couldn't the solution for the first question be: (-infinity, 0) U (0, 5) U (5.2, infinity) as that would be more specific to the fact that the inequality can be lesser than y=0, but not equal to it?

[@ShivayshKumar]

Nevermind, I understand my mistake :)

[@lemontart7319]

can we solve it by multiplying both sides by the denominator squared(we know for sure its positive cuz its a square)
and then treat it like a quadratic inequality with restrictions?

[@mshavrotscanadianuniversit6234]

Can you please let me know the time on the video that you are referring to?

[@lemontart7319]

@@mshavrotscanadianuniversit6234 the first question in the video ☺☺

[@mshavrotscanadianuniversit6234]

Sorry, I’ve been out west visiting my daughter.
What you did would help you find the x intercept but not so helpful for solving the inequality. I would stick to my method 😊

[@8nvibin454]

Do you acc need to know the horizontal asymptote for this?

[@8nvibin454]

Only if ur graphing right?

[@mshavrot_math]

Definitely if you wanted to solve by graphing.

[@tns_lover9271]

When solving interqualites what is the best way (easier way to look at it) I have a test in 2 days and I wanted to make sure that I understand how to do it

[@mshavrotscanadianuniversit6234]

Make sure that you are being very careful with the inequalities like the one that I did (5f) to make sure that you aren't missing and of the parts of the graph.