clara1223
  • clara1223
Given f(x)=-3x+(1/x)-3, simplify (f(x+h)-f(x))/h when x+4
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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Loser66
  • Loser66
Let 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
Loser66
  • Loser66
Where are you stuck?
clara1223
  • clara1223
@Loser66 I don't even know where to start...

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Loser66
  • Loser66
from f(x), make the right hand side has the same denominator, what do you get?
clara1223
  • clara1223
This 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
clara1223
  • clara1223
@Loser66
Loser66
  • Loser66
Yes, but you make the same denominator wrong!! redo it here, please
clara1223
  • clara1223
Which denominator are you talking about?
Loser66
  • Loser66
ok, let make it clear \(f(x) = -3x +\dfrac{1}{x}-3=\dfrac{-3x^2-3x+1}{x}\) ok?
Loser66
  • Loser66
Now, \(f(x+h) = \dfrac{-3(x+h)^2-3(x+h)+1}{x+h}\)
Loser66
  • Loser66
Open parentheses and Take difference \(f(x+h)-f(x) \) , we have \(\dfrac{-3(x^2+2xh+h^2)-3x-3h+1}{x+h}-\dfrac{-3x^2-3x+1}{x}\) right?
Loser66
  • Loser66
\(\dfrac{-3x^2-6xh-3h^2-3x-3h+1}{x+h}+\dfrac{3x^2+3x-1}{x}\) ok?
Loser66
  • Loser66
REMEMBER, that is just f(x+h)-f(x) , we didn't \(\div h\) yet!!!
Loser66
  • Loser66
Now, 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
  • Loser66
It becomes \(\dfrac{-3x^3-6x^2h-3xh^2-3x^2-3xh+x}{x(x+h)}+\dfrac{(x+h)(3x^2+3x+1)}{x(x+h)}\)
Loser66
  • Loser66
Simplify,
Loser66
  • Loser66
sorry, mistake at the last 1, it is -1, not 1 from numerator of the second term
clara1223
  • clara1223
I understand, keep going please, you've been incredibly helpful.
Loser66
  • Loser66
just that, you simplify, then divided by h more, then replace x =4 to get the answer.
Loser66
  • Loser66
hey, barbecue, is there any shorter way?? Please, help. My way is tooooooooooooooo long and easy get mistake. hehehe.. barbecue @dan815 Please, please
clara1223
  • clara1223
So far I have: \[\frac{ -3x ^{3}-6x ^{2}h-3xh ^{2}-3x ^{2}-3xh+x }{ x(x+h) }+\frac{ 3x ^{3}+3x ^{2}h+3x ^{2}+3xh-x-h }{ x(x+h) }\] after I canceled out: \[\frac{ 3x ^{2}h-3xh ^{2}-h }{ x(x+h) }\] Then I took h out of numerator: \[\frac{ h(3x ^{2}-3xh-1) }{ x ^{2}+xh }\] How am I doing so far?
clara1223
  • clara1223
@Loser66 what's my next step?
clara1223
  • clara1223
@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.
anonymous
  • anonymous
source:http://www.acalculator.com/math-calculators.html

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