mrs. Torres i cant begin to explain to you how much i love you for this! My pre calc teacher has went over this multiple times, and I never fully understood, but with you I understood right away. THANK YOU
this video was published years ago, so you might not see this comment but i just wanted to say thank you so much for this video. i love how you go through every small detail and explain the inbetweens rather than just jumping from one step to next. this is the first video on rationalizing that has actually helped me understand what was going on (and I've seen many). i don't usually comment on videos but i don't think the comments under this video justify how well explained and helpful this was.
...Good day Mrs.Torres, An alternative way to rationalize the numerator of your expression (sqrt(x+h) - sqrt(x))/h is by rewriting the denominator h as: h = (x + h) - x, and treating it as a difference of squares, so h = (x + h) - x = (sqrt(x+h) - sqrt(x))(sqrt(x+h) + sqrt(x)), finally after cancelling common factors of top and bottom we get the new expression: (sqrt(x+h) - sqrt(x))/h = 1/(sqrt(x+h) + sqrt(x))... Take care, Jan-W
herr schwarz So that is why you want to meet, so you can burn your short fuse. If that is the case guy, I will only meet in a public place. Only after you have calmed down.
When rationalizing the numerator why do you multiply straight accross instead of distributing it out to each one like you would with (x-1)(x+3) or something like that?
+Ray G It's a useful shortcut that works when multiplying conjugates. You could distribute them out (FOIL), and you will arrive at the same result. It's very similar to multiplying (x+2)(x-2). The shortcut is x^2-4. If you do the long way by distributing you get x^2+2x-2x-4. Notice that the terms 2x have opposing signs which means they will cancel out to zero and what's left is x^2-4. Since I know this will always happen when multiplying conjugates, I just do the shortcut. You square the first term and the last term and the result has a minus sign between the two terms. Hope this helps.
mrs. Torres i cant begin to explain to you how much i love you for this! My pre calc teacher has went over this multiple times, and I never fully understood, but with you I understood right away. THANK YOU
This is the best most thoroughly explained math lesson I have seen.
I agree
this video was published years ago, so you might not see this comment but i just wanted to say thank you so much for this video. i love how you go through every small detail and explain the inbetweens rather than just jumping from one step to next. this is the first video on rationalizing that has actually helped me understand what was going on (and I've seen many). i don't usually comment on videos but i don't think the comments under this video justify how well explained and helpful this was.
Thank you!! 😊 So glad this video was so helpful to you.
This was so simple and clear! Thank you for showing us that shortcut(:
Outstanding detail! Thank you kindly!
Thank you!
...Good day Mrs.Torres, An alternative way to rationalize the numerator of your expression (sqrt(x+h) - sqrt(x))/h is by rewriting the denominator h as: h = (x + h) - x, and treating it as a difference of squares, so h = (x + h) - x = (sqrt(x+h) - sqrt(x))(sqrt(x+h) + sqrt(x)), finally after cancelling common factors of top and bottom we get the new expression: (sqrt(x+h) - sqrt(x))/h = 1/(sqrt(x+h) + sqrt(x))... Take care, Jan-W
Nice!! Your approach is very interesting. Thank you!
I teach this in precalculus to 11 and 12th graders.
XD suddenly forget how to rationalizing this kind of problem and it helps me a lot. thx ~~
Thank you very much!
Thank you!!!
Thank you so much you are a life saver :D!!!
glad you like.
Thanks! You saved my life!
oh my life calculus was a drag until this!
herr schwarz who are you, again?
herr schwarz You seem angry.
herr schwarz Well, now that you feel better, tschüss.
herr schwarz So that is why you want to meet, so you can burn your short fuse. If that is the case guy, I will only meet in a public place. Only after you have calmed down.
herr schwarz Hmm, I do not know. I will remain weary of you.
I just want to say thank you
Big help!!
When rationalizing the numerator why do you multiply straight accross instead of distributing it out to each one like you would with (x-1)(x+3) or something like that?
+Ray G It's a useful shortcut that works when multiplying conjugates. You could distribute them out (FOIL), and you will arrive at the same result. It's very similar to multiplying (x+2)(x-2). The shortcut is x^2-4. If you do the long way by distributing you get x^2+2x-2x-4. Notice that the terms 2x have opposing signs which means they will cancel out to zero and what's left is x^2-4. Since I know this will always happen when multiplying conjugates, I just do the shortcut. You square the first term and the last term and the result has a minus sign between the two terms. Hope this helps.
great help
is this for calculus??? i thought i was preparing for my exam coz im in 8th grade, my exams tomorrow done nothing so looking for online tutorials
way over complicated, its simple algebra