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clara1223
 one year ago
Given f(x)=3x+(1/x)3, simplify (f(x+h)f(x))/h when x+4
clara1223
 one year ago
Given f(x)=3x+(1/x)3, simplify (f(x+h)f(x))/h when x+4

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Loser66
 one year ago
Best ResponseYou've already chosen the best response.3Let me help you write it in neat \(f(x) = 3x+\dfrac{1}{x}3 \) Simplify\( \dfrac{f(x+h)f(x)}{h} \) when x = 4

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0@Loser66 I don't even know where to start...

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3from f(x), make the right hand side has the same denominator, what do you get?

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0This is what I brainstormed so far, but I am not sure if this is anywhere close to the right track. Plus, it doesn't look like any of the answer choices

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3Yes, but you make the same denominator wrong!! redo it here, please

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0Which denominator are you talking about?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3ok, let make it clear \(f(x) = 3x +\dfrac{1}{x}3=\dfrac{3x^23x+1}{x}\) ok?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3Now, \(f(x+h) = \dfrac{3(x+h)^23(x+h)+1}{x+h}\)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3Open parentheses and Take difference \(f(x+h)f(x) \) , we have \(\dfrac{3(x^2+2xh+h^2)3x3h+1}{x+h}\dfrac{3x^23x+1}{x}\) right?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3\(\dfrac{3x^26xh3h^23x3h+1}{x+h}+\dfrac{3x^2+3x1}{x}\) ok?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3REMEMBER, that is just f(x+h)f(x) , we didn't \(\div h\) yet!!!

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3Now, we have 2 fractions with different denominator; We need make them have the same denominator by multiply the first term by x, the second term by (x+h)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3It becomes \(\dfrac{3x^36x^2h3xh^23x^23xh+x}{x(x+h)}+\dfrac{(x+h)(3x^2+3x+1)}{x(x+h)}\)

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3sorry, mistake at the last 1, it is 1, not 1 from numerator of the second term

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0I understand, keep going please, you've been incredibly helpful.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3just that, you simplify, then divided by h more, then replace x =4 to get the answer.

Loser66
 one year ago
Best ResponseYou've already chosen the best response.3hey, barbecue, is there any shorter way?? Please, help. My way is tooooooooooooooo long and easy get mistake. hehehe.. barbecue @dan815 Please, please

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0So far I have: \[\frac{ 3x ^{3}6x ^{2}h3xh ^{2}3x ^{2}3xh+x }{ x(x+h) }+\frac{ 3x ^{3}+3x ^{2}h+3x ^{2}+3xhxh }{ x(x+h) }\] after I canceled out: \[\frac{ 3x ^{2}h3xh ^{2}h }{ x(x+h) }\] Then I took h out of numerator: \[\frac{ h(3x ^{2}3xh1) }{ x ^{2}+xh }\] How am I doing so far?

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0@Loser66 what's my next step?

clara1223
 one year ago
Best ResponseYou've already chosen the best response.0@dan815 can you help me? @loser66 was very helpful but he's right, his way is very long and complicated and I still am not clear on the subject.
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