Forgotten Fractions? Get Guidance Here!

AI Thread Summary
The discussion revolves around solving a complex equation involving fractions and powers of x. A participant initially arrived at an answer of 0.4 but struggled with the fundamentals of fractions and isolating x. Suggestions included using the reciprocal for division, factoring out common terms, and simplifying the equation by reducing terms like 4-2x and 3-3x. Despite attempts to factor and simplify, the participant faced difficulties due to the presence of multiple powers of x, leading to confusion in isolating the variable. The conversation emphasizes the need for a systematic approach to tackle equations with varying degrees of x.
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http://img340.imageshack.us/img340/1967/25616732jw6.jpg

i got answer of 0.4
by trial and error, but i have seem to forgotten the basic of fraction...

please guide me thanks
 
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Dividing by something is the same as multiplying by that something's reciprocal.
 
i have tried that but still the power is larger than a quadratic, so i wasnt able to solve it
 
Reduce the 4-2x terms and also with the left over 4-2x you can factor out a common term of 2.

Factor our a common term of 3 in 3-3x and keep going from there.
 
Another tip is to square root both sides to get rid of the even powers larger than 2 after you've done all that.
 
did factor out the 3 it becomes 27, i think
and canceled some of the 4-2x , as you suggested

but the main problem for me is still so much x,
cant really isolate it, because i tried expanding it
and i get like x^1 , x^2, x^3, X^4...
and do not know how to solve those
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Essentially I just have this problem that I'm stuck on, on a sheet about complex numbers: Show that, for ##|r|<1,## $$1+r\cos(x)+r^2\cos(2x)+r^3\cos(3x)...=\frac{1-r\cos(x)}{1-2r\cos(x)+r^2}$$ My first thought was to express it as a geometric series, where the real part of the sum of the series would be the series you see above: $$1+re^{ix}+r^2e^{2ix}+r^3e^{3ix}...$$ The sum of this series is just: $$\frac{(re^{ix})^n-1}{re^{ix} - 1}$$ I'm having some trouble trying to figure out what to...

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