A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
can someone explain to me how to do this problem? will give medals! (problem is in picture below)
anonymous
 one year ago
can someone explain to me how to do this problem? will give medals! (problem is in picture below)

This Question is Closed

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.0your problem is very interesting how do you propose solving it if you were to figure it out?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so \[f(a) = \frac{4a}{a7}\]\[f(a+h) = \frac{4a+4h}{a+h+7}\] therefore... \[\frac{f(a+h)f(a)}{h} = \frac{\dfrac{4a+4h}{a+h+7}  \dfrac{4a}{a7}}{h}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So forget the \(h\) at the bottom for now and concentrate on finding an LCD between \(a+h+7\) and \(a7\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[ \frac{f(a+h)f(a)}{h} = \frac{\dfrac{4a+4h}{a+h7}  \dfrac{4a}{a7}}{h}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh okay i see where this is going, the initial start confused me, i forgot which way to plug it in. oh and jhannybean. youre always to my rescue! you helped me understand things well enough yto get to precalc, so thanks!!

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.0thank you, beanerwoman

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you should be a teacher

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.0she shouldn't like for real ;) she should be the CEO of openstudy

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So let's finish this badboy.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What did you get as your LCD?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0cant you multiply whole thing by (a+h7)and(a7)? ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yup, That's what I got \[\frac{(a7)(4a+4h)4a(a+h7)}{(a7)(a+h7)}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then it all cancels, well most of it, right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No no, it doesn't all cancel. we have to expand it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah im lost again :(

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0buut doesnt the denominator go away?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No, we're trying to find an LCD by multiplying both of the denominators of the two fractions with eachother, we can't simply cancel them otherwise there would be no point of finding the LCD in the first place!

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.0show that it goes away

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And remember, we're still dividing EVERYTHING by h, so we need to expand our function to see which h values are still left :D

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'llcompare it with mine :) one minute!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i think i did somehing wrong

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then i distribute negative here? :

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then i cancel out terms?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah I found where I had messed up too haha

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.0perform the operation instead of using the word cancel

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{(a7)(4a+4h)4a(a+h7)}{(a7)(a+h7)}\]\[=\frac{4a^2+4ah28a28h4a^24ah+28a}{a^2+ah7a7a7h+49}\]\[=\frac{\cancel{4a^2}\cancel{+4ah}\cancel{28a}28h\cancel{4a^2}\cancel{4ah}\cancel{+28a}}{a^2+ah7a7a7h+49}\]\[=\frac{28h}{a^2+ah14a7h+49}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So now all of this is divided by h.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[=\dfrac{\dfrac{28h}{a^2+ah14a7h+49}}{h}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That means we're multiplying in h throughout the entire denominator.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0why are we multiplying it through the denominator only?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Its a rule in dividing fractions: \(\dfrac{\dfrac{a}{b}}{c} \iff \dfrac{a}{bc} \)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh wow i didnt know that

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And actually, I just realized we don't eve have to multiply through the denominator, we can just leave it alone.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It would look like: \[\dfrac{\dfrac{28h}{a^2+ah14a7h+49}}{h} \longrightarrow \frac{28h}{h(a^2+ah14a7h+49)}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so what do we do with the denominator now? thi is super intense 0_0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And therefore, because we're multiplying both the numerator AND denominator by h, we can eliminate the h altogether. \[\frac{28\cancel{h}}{\cancel{h}(a^2+ah14a7h+49)} =\boxed{ \frac{28}{a^2+ah14a7h+49}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0holy rap girl. youre a genius... im gonna have to study this one.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So now we can state that \[\boxed{\frac{f(a+h)f(a)}{h} = \frac{\dfrac{4a+4h}{a+h7}  \dfrac{4a}{a7}}{h} = \frac{28}{a^2+ah14a7h+49}}\]

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.0jhan, that looks pretty

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i would have never gotten this...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0More importantly, do you understand my steps?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes, and ive screenshotted all of them. im going to rewrite them all in my notes with your steps, i forgot about the division rule!!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah that's important \(\checkmark\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0pretty much, we plugged in those functions in for x, got lcd common denominators, combined like terms, divided all by h in which we innstead, multiplied, then canceled out terms (h in num + denom)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.