Simplify

- anonymous

Simplify

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- anonymous

\[\frac{ 2x }{ 4\pi }+ \frac{ 1-x }{ 2 }\]

- hartnn

is that really \(\pi\) in the denominator of 1st fraction ?

- anonymous

yes

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## More answers

- hartnn

now we have to make the denominator common , so we need to multiply and divide by 2\(\pi\) in 2nd fraction to get 4\(\pi\)as common denominator .
\(\huge\frac{2x}{4\pi}+\frac{2\pi(1-x)}{4\pi}\)
now can u solve further ??

- anonymous

i got up to \[\frac{ x-pix }{ 2\pi} = 1/2\]

- anonymous

i mean -1/2

- hartnn

nopes,
\(\huge\frac{2x}{4\pi}+\frac{2\pi(1-x)}{4\pi}=\frac{2x+2\pi(1-x)}{4\pi}=\frac{x+\pi-\pi x}{2\pi}\)
u can't simplify it further.

- anonymous

i forgot one important thing. the equation is equal to zero. and i'm solving for x

- hartnn

okay, so it will be
\(\huge x+\pi-\pi x=0 \implies x(1-\pi)=-\pi \\\huge x=\frac{-\pi}{1-\pi}or\frac{\pi}{\pi-1}\)

- anonymous

so was my step right so far?

- hartnn

u got -1/2, but its actually, pi/(pi-1)

- anonymous

equal to zero? my teacher did the same thing as me.. but i didn't write the last part leading towards the answer.

- anonymous

i crossed multiply
\[\frac{ 4x }{ 8\pi } + \frac{ 4\pi - 4pix }{ 8\pi } = 0\]

- anonymous

i split the equation up also

- hartnn

the first term has 'x'

- anonymous

the i got \[\frac{ x }{ 2\pi } - \frac{ \pi }{ 2\pi } = -1/2 \]

- anonymous

the \[\frac{ \pi }{ 2 reduces to 1/2 and i brought it over...

- hartnn

but u cannot cancel pi, the first term had x in it, not pi.

- anonymous

yes... and i'm solving for it. i haven't found the answer further than that step

- anonymous

what are you talking about cancel? i didn't cancel anything other than the pis... which was pi/2pi... they're in common? this part i know for sure is right. i don't know how to get after that

- hartnn

how did u get -1/2 ...and where did your 8 go from denominator ?

- anonymous

that was a typo. and i reduced \[\frac{ \pi }{ 2\pi } \] to get 1/2 and then i subtracted it on both sides so the equation is equal to -1/2

- anonymous

i'm basically trying to isolate the x as much as possible

- hartnn

\(\huge \frac{ 4x }{ 8\pi } + \frac{ 4\pi - 4\pi x }{ 8\pi } = 0\)
u had this correct.
then u separated denominator u should get,
\(\large \frac{x}{2\pi}+\frac{1}{2}-\frac{x}{2}=0\)
but this is not the best way to isolate x.

- anonymous

yea, but it's easier for me to visualize it. instead of clutter i wanted to separate the fractions

- hartnn

ok, so continuing with separating the fraction, you can cancel all the 2's in the denominator(equivalent to multiplying 2 on both sides.)
then shifting +1to other side, u get
\(\large x(\frac{1}{\pi}-1)=-1\)
which again gives,
\(\large x=\frac{-1}{1/\pi-1}=\frac{\pi}{\pi-1}\)

- hartnn

- anonymous

so i multiply the top and bottom by 2pi to get rid of it in the denominator?

- anonymous

where do you get +1?

- hartnn

yes, u can do that also, that will lead to same answer.

- hartnn

as i said, i multiplied both sides by 2

- hartnn

as i said, i multiplied both sides by 2

- anonymous

\[\frac{ 2x }{ 4\pi }+ \frac{ 1-x }{ 2 }\] is not an equation. there is nothing to "solve" for
you can add however, by finding the lcd is \(4\pi \) and adding

- anonymous

you would get
\[\frac{2x+2(1-x)}{4\pi}\]

- anonymous

i got x = \[\frac{ \pi }{ 1-\pi }\]

- anonymous

- pi / 1-pi = pi / 1+pi

- hartnn

there must be slight error in minus sign, its pi/(pi-1)

- anonymous

no, i subtracted 1/2 from both sides and it was -1/2

- anonymous

then i multiplied both sides by 2pi which made it -pi.

- anonymous

so i got \[x - pix = -pi\]

- hartnn

both those steps are correct.
u get x(1-pi)=-pi
x=-pi/(1-pi) = pi/(pi-1)

- anonymous

then i factored out the x. \[x(1-\pi) = -\pi \]
\[x = \frac{ -\pi }{ 1-\pi } \]

- hartnn

yes so its -pi/(1-pi) which is same as pi/(pi-1)

- anonymous

are you sure? if you take out the negative, wouldn't the denominator be 1+ pi?

- hartnn

nopes it would not be 1+pi.
it will be pi-1
-(1-pi) = pi-1
yes, sure.

- anonymous

ok i see you flipped it around. lol

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