I've been trying to do this question for well over 2 hours. My friends have tried to help me, but I rejected them, believing I could do it myself. I do realize that the majority of users here are of a college/university math level...so I hope you can understand that we were all once fucking confused and help me out here.
Solve.
x+2 / x-1 + x-4 / x+2 = x+1/x-1 + 1/2
I have the answer, but I don't know how to solve it. Thanks.
Name:
Anonymous2006-11-21 2:42
Whoops, tis
(x+2/x-1) + (x-4/x+2) = (x+1/x-1) + (1/2)
Name:
Anonymous2006-11-21 2:57
First, multiply both sides by the common denominator (x-1)(x+2):
(x+2)(x+2) + (x-4)(x-1) = (x+1)(x+2) + 1/2*(x+2)(x-1)
>>8
Well, I saw >>1 and thought he must've forgot to put brackets around the spaced apart thingies. Then I saw >>2 and I was confused, because it seemed to imply the lack of brackets was intentional since
(x+2/x-1) + (x-4/x+2) == x+2 / x-1 + x-4 / x+2
but
(x+2/x-1) + (x-4/x+2) != (x+2)/(x-1) + (x-4)/(x+2).
And now I'm retarded? Just learn how to use the notation properly, kthx.
Name:
4tran2006-11-24 1:11
>>9
(x+2/x-1)==(x+2)/(x-1) almost always, but the former is not "proper math notation", though often used anyway so the place doesn't get clutterred by parentheses.
(x+2/x-1)==x+(2/x)-1 is rare (though technically correct "math notation"), and generally bad style
Name:
Anonymous2006-11-24 2:17
>>10
I don't know what country you're from, but over here (x+2/x-1) is always x+(2/x)-1. We call it 'precedence' and it makes equations unambiguous.
Name:
4tran2006-11-24 4:56
I know of such a thing as precedence, but my point is that on the internet/other medium that involves typing, sometimes common sense > precdence
f^-1 is the inverse function of f lol lol see it's -1 lol irony
...but sin^-1 is csc, gotcha!
sin is a function
...but since we like it a lot we omit parenthesis lol lol sin x
We're to lazy to write a dot for multiplication; can you imagine how tiring could that be?
...so when you say asinx you mean a · sin(x)... or was it arcsin(x)? Oh, wait, I think it means a·s·i·n·x... oh shi-
Name:
Anonymous2006-11-25 19:35
ive never seen anyone refer to csc(x) as sin^-1(x), sometimes sin(x)^-1, which is consistent and makes sense.
f^-1(x) != f(x)^-1
theyre two separate concepts, if you see them used interchangably its because whoever is presenting them doesn't understand what the notation means.
i agree that writing sin x is being loose though, and most teachers who pay attention will use parentheses because they recognize that it is a function.
to illustrate the inequality
suppose f(x) = x + 3
f^-1(x) = x - 3
satisfies f^-1(f(x)) = x
>>16 f^-1(x) != f(x)^-1
That's what I'd hope, but maths teachers will omit the parenthesis for well-known functions such as sin, cos, tan, etc., and so, when they need to do sin(x)², they write sin²x (because it'd otherwise be confused with sin(x²)). Then they use csc to avoid writing sin^-1, but see what I mean.
>>17
Are you saying it's a "special case"? Proper syntax must not have "special cases".
Maths notation was designed by Larry Wall.
Name:
Anonymous2006-11-26 10:05
>>19
Math syntax is not meant to be read by a computer you stupid retard.
Name:
Anonymous2006-11-26 10:50
>>19
This is not a case of intelligent design, the notation has evolved over thousands of years. There's bound to be some weirdness to it.
Still, consciously introducing ambiguity cannot be justified.