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x3_drummerchick
 one year ago
can someone explain to me how to do this problem? will give medals! (problem is in picture below)
x3_drummerchick
 one year ago
can someone explain to me how to do this problem? will give medals! (problem is in picture below)

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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?

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

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4So forget the \(h\) at the bottom for now and concentrate on finding an LCD between \(a+h+7\) and \(a7\)

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

x3_drummerchick
 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

x3_drummerchick
 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

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4So let's finish this badboy.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4What did you get as your LCD?

x3_drummerchick
 one year ago
Best ResponseYou've already chosen the best response.0cant you multiply whole thing by (a+h7)and(a7)? ?

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

x3_drummerchick
 one year ago
Best ResponseYou've already chosen the best response.0then it all cancels, well most of it, right?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4No no, it doesn't all cancel. we have to expand it

x3_drummerchick
 one year ago
Best ResponseYou've already chosen the best response.0yeah im lost again :(

x3_drummerchick
 one year ago
Best ResponseYou've already chosen the best response.0buut doesnt the denominator go away?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4No, 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

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4And remember, we're still dividing EVERYTHING by h, so we need to expand our function to see which h values are still left :D

x3_drummerchick
 one year ago
Best ResponseYou've already chosen the best response.0is this right?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4I'llcompare it with mine :) one minute!

x3_drummerchick
 one year ago
Best ResponseYou've already chosen the best response.0i think i did somehing wrong

x3_drummerchick
 one year ago
Best ResponseYou've already chosen the best response.0then i distribute negative here? :

x3_drummerchick
 one year ago
Best ResponseYou've already chosen the best response.0then i cancel out terms?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4Yeah 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

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

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4So now all of this is divided by h.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4\[=\dfrac{\dfrac{28h}{a^2+ah14a7h+49}}{h}\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4That means we're multiplying in h throughout the entire denominator.

x3_drummerchick
 one year ago
Best ResponseYou've already chosen the best response.0why are we multiplying it through the denominator only?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4Its a rule in dividing fractions: \(\dfrac{\dfrac{a}{b}}{c} \iff \dfrac{a}{bc} \)

x3_drummerchick
 one year ago
Best ResponseYou've already chosen the best response.0oh wow i didnt know that

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4And actually, I just realized we don't eve have to multiply through the denominator, we can just leave it alone.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4It would look like: \[\dfrac{\dfrac{28h}{a^2+ah14a7h+49}}{h} \longrightarrow \frac{28h}{h(a^2+ah14a7h+49)}\]

x3_drummerchick
 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

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4And therefore, because we're multiplying both the numerator AND denominator by h, we can eliminate the h altogether. \[\frac{28\cancel{h}}{\cancel{h}(a^2+ah14a7h+49)} =\boxed{ \frac{28}{a^2+ah14a7h+49}}\]

x3_drummerchick
 one year ago
Best ResponseYou've already chosen the best response.0holy rap girl. youre a genius... im gonna have to study this one.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4So 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

x3_drummerchick
 one year ago
Best ResponseYou've already chosen the best response.0i would have never gotten this...

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4More importantly, do you understand my steps?

x3_drummerchick
 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!!

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.4Yeah that's important \(\checkmark\)

x3_drummerchick
 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)
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