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

1. 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

2. Loser66

Where are you stuck?

3. clara1223

@Loser66 I don't even know where to start...

4. Loser66

from f(x), make the right hand side has the same denominator, what do you get?

5. 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

6. clara1223

@Loser66

7. Loser66

Yes, but you make the same denominator wrong!! redo it here, please

8. clara1223

Which denominator are you talking about?

9. Loser66

ok, let make it clear $$f(x) = -3x +\dfrac{1}{x}-3=\dfrac{-3x^2-3x+1}{x}$$ ok?

10. Loser66

Now, $$f(x+h) = \dfrac{-3(x+h)^2-3(x+h)+1}{x+h}$$

11. 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?

12. Loser66

$$\dfrac{-3x^2-6xh-3h^2-3x-3h+1}{x+h}+\dfrac{3x^2+3x-1}{x}$$ ok?

13. Loser66

REMEMBER, that is just f(x+h)-f(x) , we didn't $$\div h$$ yet!!!

14. 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)

15. Loser66

It becomes $$\dfrac{-3x^3-6x^2h-3xh^2-3x^2-3xh+x}{x(x+h)}+\dfrac{(x+h)(3x^2+3x+1)}{x(x+h)}$$

16. Loser66

Simplify,

17. Loser66

sorry, mistake at the last 1, it is -1, not 1 from numerator of the second term

18. clara1223

19. Loser66

just that, you simplify, then divided by h more, then replace x =4 to get the answer.

20. Loser66

hey, barbecue, is there any shorter way?? Please, help. My way is tooooooooooooooo long and easy get mistake. hehehe.. barbecue @dan815 Please, please

21. 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?

22. clara1223

@Loser66 what's my next step?

23. 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.

24. anonymous

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