(infinity) - (1 / infinity) = X      What is the variable " X " Equal to?
606683
The factor (1/infinity) equals to zero.\n\nHence the term\n\n(infinity) - (1/infinity) = (infinity) - 0\n\nTherefore,\n\nX = infinity
602488
1-x = -(x-1)\nx^3 - 1 = (x-1)(x^2+x+1)\nAnswer: -(x-1)(x^2+x+1)
1187309
I think I did it.  If y=1/log(x), then a few manipulations gave me\n\nx=10^(1/y).\n\nI'm assuming by log you mean log to the base 10.  I suppose mathematicians will start fussing about what happens at y=0, but a physicist like me doesn't worry that much about infinities ...
668466
Let x = 0.999...\n\n10x = 9.999....\n\n10x - x = 9.999... - 0.999...\n\n9x = 9\n\nx = 1.\n\nThis is the 3rd time in two weeks I've encountered this question here. So next time this is posted, do me the favor of answering it.
846663
(x+3)(x-1)\n\n x= -3\nx=1
200150
for all of those, all u do is set once variable at a time equal to zero. for instance..\n\n-x+0=2\n-x=2  <--- multiply x and 2 by -1\nx=2\n\nthen..\n\n0+y=2\ny=2
807939
= (1 + 8x)*(1 - 8x) = 1 - 64*x^2\n\nAnd what do you say?
884322
(x+2)/(x+2)(x+3)=\n1/x+3
46798
if (1/x) + 2= (c/2)\n--------------------------------\n\n1/x = (c/2) - 2\n----------------------\nx = 1/((c/2) - 2)\n       (OR)\nx = ((c/2)-2)^-1\n-----------------------
800627
x = 3/(x-2)\n\n=> x(x-2) = 3\n=> x^2 - 2x = 3\n=> x^2 - 2x - 3 = 0\n=> (x-3) (x+1) = 0\n\nEither x-3 = 0 => x=3\nOr x+1 = 0 => x=-1
537832
(x/x-2)-(x+1/x)=8/(x^2-2x)\n[x(x)-(x-2)(x+1)]/[x(x-2)]=8/[x(x-2)]\nx^2-(x^2-2x+x-2)=8\nx^2-x^2+x+2=8\nx=8-2=6
872873
There is only one value that works: \nx=1\n\nj
904022
Surprisingly, yes.  This bugged the heck out of me in middle school, but it's a consequence of the way infinity works.\n\nThe classic proof is:\n\n    x = 0.999999....\n10x = 9.999999....\n\nSubtract the first line from the second, and you get\n\n9x = 9, therefore x = 1.
32703
Infinity\n\nAddendum:\n\nI was astonished to see that the majority of answers are not converging on infinity, as I had learned in school. So I did a little more research. \n\nIt definitely remains as the mathematical definition that Z/0 = infinity for any non zero value of Z. However, as computers cannot process infinity, calculators etc., all show error or undefined. Modern applied mathematics are now teaching contexts where the result is defined and contexts where it should be considered undefined.\n\nAlthough its clear infinity is still the text book answer, it is also clear than in a practical sense infinity has no value and you still need to code around the case in your calculation software.\n\nLook below for many of the sites that discuss this.
81372
I don't mean to be rude, but none of the above answers are quite right, and some are actually quite wrong. 0/0 is not undefined, 0/0 is not always infinity, 0/0 never means "nothing" (in fact, it is used quite frequently in calculus), and although there is no general way to define 0/0, it most certainly can be defined given enough information in a problem.\n\nNormlparker had it closest, when discussing the nature of division. In other words, 10/2 means take 10 things and divide them into 2 equal groups; when you do, each of those groups will contain 5 things, so 10/2=5. Dividing by 0 doesn't conceptually make sense. You can't take 10 things and divide them into no groups. That answer is UNDEFINED. (Captial letters for vocabulary emphasis, not because I am yelling.)\n\nNow dividing 0 by 0 is a different issue, because you can surely take no things and make them into no groups. However, what's the size of those nonexistent groups? It's not infinity, nor is it undefined, as some previous posters have said. Dividing 0 by 0 is an INDETERMINATE value, and it's exactly as you said--it could equal just about anything.\n\nTake for instance the fraction (x^2+2x-3)/(x-1). If you plug x=1 into the fraction, you get 0/0, but the function is definitely not infinity when you get close to x=1. If you factor the numerator, the fraction becomes [(x+3)(x-1)]/(x-1). Cancel those common factors and you get x+3. In other words, this fraction (although undefined at x=1) gets very close to x+3=1+3=4. In this case, 0/0 is basically 4.\n\nTo be specific, a non-zero number divided by 0 approaches infinity (or negative infinity), but 0/0 can approach lots of things. However, ANYTHING divided by 0 is not a real number. \n\nWhen you took your equation (0)(0)=0 and divided both sides by one of the 0s on the left side, you actually violated a mathematical principle. Sure you can divide both sides of an equation by any number, as long as you are certain that number is not 0.\n\nSome of the most famous mathematical fallacies are based upon divideng by 0 in a sneaky way. You can prove lots of untrue things (such as 1=2) if you do that, and it's actually kind of fun. I used to do that once a year in my geometry classes to "prove" to my students all math was worthless, and as soon as they got excited, I showed them how I fooled them. They usually didn't care so much, but nerds like me think that kind of stuff is hilarious.\n\nHere are some other indeterminate values that can equal anything: (0)(infinity), 1^(infinity), (infinity)/(infinity).
605811
As Lauren said, it's 1/x.\n\nMemorize this. It will be very useful.
491455
(x^2+4x+1)/(x-2) = x+2+3/(x-2)\n\nx  : x^2+4x+1-x^2-2x =2x+1\n2  : 2x+1 -2x-4 =3