sci, i do not understand what's going on there
[math]\[\frac{x+\sqrt{x^{2}-1}}{x}\]=\[1+\sqrt{1-\frac{1}{x^{2}}}\] [/math]
how does the simplification work here?
>>7667495
[eqn]\[\frac{x+\sqrt{x^{2}-1}}{x}\] [/eqn]
>>7667499
[math]\[\frac{x+\sqrt{x^{2}-1}}{x}\][/math]
>>7667501
[math]$\[\frac{x+\sqrt{x^{2}-1}}{x}\][/math]
>>7667502
MOTHER FUCKER
>>7667506
are you retarded?
wtf happened to writing jsmath equations on this site?
It's been broken for about a month now.
>>7667754
do you consistently check if your code works in your texeditor?
>>7667506
Factor out [math]x[/math] from the radical.
Divide 2 terms by [math]x[/math].
[math]\sqrt{x^2 -1} = x\sqrt{1 - \frac{1}{x^2}}[/math]
>>7667811
let's see if this works,
if it doesn't work all the raw code
including math and slashmath
are just shown instead of being interpreted:
[math]1+\frac{1}{2}=\frac{3}{2}[/math]
>>7667796
>if it doesn't work all the raw code
>including math and slashmath
>are just shown instead of being interpreted:
[math]1+\frac{1}{2}=\frac{3}{2}[/math]
[eqn]1+\frac{1}{2}=\frac{3}{2}[/eqn]
>>7668134
honestly i'm missing something here
how do we get from
[eqn]\frac{\sqrt{x^2 -1}}{x} [/eqn]
to
[eqn]\sqrt{1 - \frac{1}{x^2}}[/eqn]
do a right click on the equation, copy the tex code of the equation, put it in eqn tags and it works
>>7668151
x = sqrt(x^2) right? put that in the denominator and take it from there champ.
>>7668158
god i feel stupid
thank you
Dude, just divide by x you scrub
>>7668166
hey man, at least you didn't ask how x / x simplified to 1 :^)
i have more questions...
[eqn]\frac{x^2+xln(x)}{x+1}[/eqn]
how does it reduces to
[eqn]\frac{x^2(1+\frac{lnx}{x})}{x(1+\frac{1}{x})}[/eqn]
>>7668881
how does it reduces to
[eqn]\frac{x^2(1+\frac{lnx}{x})}{x(1+\frac{1}{x})}[/eqn]
>preview displays correctly
>posts doesn't
why
>>7668881
>how does it reduces to
>>7668133
That's essentially what he showed you.
>>7668955
yeah i realized as i posted that there was factorisation going on there
>>7668890
They just factored the top and bottom.
You really can't be old enough to post here.
>>7668885
It's the way 4chan parses the TeX, you need to throw in white space errywhere near all the commands. Now lets see if I can do it without looking like a tool: [eqn] \frac{x^2 \left( 1+ \frac{ \ln(x) }{x} \right)}{ x \left( 1 + \frac{1}{x} \right)} [/eqn]
There's a neat little theorem I came up with that relates to this subject. Let f(x) be an invertible function.
Then a*f(x) = f(f'(a)*x), where f' is the inverse of f(x).
It's essentially what you do when multiplying x with sqrt(x): f'(x) = x^2 and then it works
>>7669184
f(x)=x+1
a*f(x)=ax+a != f((a-1)*x)=ax-x+1
Not op here. I swear.
I have an issue in the same vein as OP's. How do i go from this
[eqn] \frac{ xlnx }{ \sqrt{ x } } [/eqn]
to this
[eqn] \sqrt{x} * ln x [/eqn]
>>7669457
You learn grade school algebra you fucking dumbass.
>>7669457
x/sqrt x=sqrt x
or for retards
x/sqrt x=x*x^(-1/2)=x^(1-1/2)=x^(1/2)=sqrt x
![1421218821655[1].jpg](https://i.imgur.com/ZnSQzrF.jpg "1421218821655[1]")