can you help me to slove this please ?

As I don't know where the problem lies you are going to have to tell us what you already know how to do.

Hint: You have an expression for f(x). So plug it into [imath]\dfrac{ f(x) - \dfrac{2}{9} }{x + 2}[/imath]. I don't see that it can be simplified more than "getting rid" of the fractions in the numerator.

Show us what you get when you try it.

-Dan

Addendum: Nice job with the parentheses! We've recently been having issues over problems quoted from textbooks that don't use them properly.
 
soufiane said:
f(x)=(√(1-4x) -3)/(x^2+x-2)
find:lim x tends to -2 of (f(x)-2/9)/(x+2)
Click to expand...
Please show us whatever you are able to do, or ask specific questions. You've read the posting guidelines, right?

I would first try finding the limit of f(x) itself as x approaches -2. If that turns out to be 2/9, then what you are asked for looks like the derivative!
 
\(\displaystyle f(x)- 2/9= \frac{\sqrt{1- 4x}- 3}{x^2+ x- 2}- 2/9\)

Get common denominator 9(x^2+ x- 2).
\(\displaystyle \frac{9(\sqrt{1- 4x}- 3)- 2x^2- 3x+ 4}{9x^2+ 9x- 18}\)
\(\displaystyle = \frac{9\sqrt{1- 4x}-27- 2x^2- 3x+ 4}{9x^2+ 9x- 18}\)
\(\displaystyle = \frac{9\sqrt{1- 4x}- 2x^2- 3x- 23}{9x^2+ 9x- 18}\)

Now divide by x+ 2.
\(\displaystyle = \frac{9\sqrt{1- 4x}- 2x^2- 3x- 23}{(x+ 2)(9x^2+ 9x- 18)}\)
\(\displaystyle = \frac{9\sqrt{1- 4x}- 2x^2- 3x- 23}{9x^3+ 27x^2+ 36x- 36}\)
 
soufiane said:
f(x)=(√(1-4x) -3)/(x^2+x-2)
find: (f(x)-2/9)/(x+2)
Click to expand...
Hi soufiane. Did this problem arise from working on something else, or was it assigned to you as is? (To me, it seems a peculiar exercise to assign, yet it could be valid practice.) Also, please check that you've posted everything correctly. Thanks!

HallsofIvy's worked solution follows the same approach that I would use, but his result contains two mistakes. There's a minor arithmetic error in his first step: the -3x term in the numerator ought to be -2x. I'm not sure how he obtained the 36x term in the denominator, but it needs to be removed.

Unless I'm instructed otherwise, I usually write the final denominator in factored form (when possible), but that's a personal choice.

If you need help understanding the work shown, please let us know what kind of experience you have working with algebraic ratios or tell us what your math class has been doing. If you'd like us to check any work, then please post it.

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This was posted three times under different subjects; but the third time it was presented as a limit problem:

can you help me to solve this, please?

f(x)=(√(1-4x) -3)/(x^2+x-2) find:lim x tends to -2 of (f(x)-2/9)/(x+2)
www.freemathhelp.com

There, I pointed out that the expression would be interesting if the limit of f(x) was 2/9; in fact it is. So that's what needs to be done.
 
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