# Simple Algebra Problem **URL:** \ **Category:** Factual Questions\ **Created:** [January 30, 2003, 1:58am UTC](https://boards.straightdope.com/t/simple-algebra-problem/151494 "2003-01-30T01:58:57Z")\ **Posts on this page:** 15\ **Page:** 2
**Author:** ![dylan\_73](https://avatars.discourse-cdn.com/v4/letter/d/ecccb3/32.png) [@dylan\_73](https://boards.straightdope.com/u/dylan_73)\ **Post date:** [January 30, 2003, 1:25pm UTC](https://boards.straightdope.com/t/simple-algebra-problem/151494/21 "2003-01-30T13:25:42Z")
```php Is this the only way to show it? Type a[sup]2[/sup]... ``` ---
**Author:** ![Johnny\_L.A](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/johnny_l.a/32/1084_2.png) [@Johnny\_L.A](https://boards.straightdope.com/u/Johnny_L.A)\ **Post date:** [January 30, 2003, 1:33pm UTC](https://boards.straightdope.com/t/simple-algebra-problem/151494/22 "2003-01-30T13:33:28Z")
:smack: Why didn’t I think of that? (I tried using the “code” tags but they didn’t work the way I wanted them to.) ---
**Author:** ![Urban\_Ranger](https://avatars.discourse-cdn.com/v4/letter/u/e9c0ed/32.png) [@Urban\_Ranger](https://boards.straightdope.com/u/Urban_Ranger)\ **Post date:** [January 30, 2003, 3:45pm UTC](https://boards.straightdope.com/t/simple-algebra-problem/151494/23 "2003-01-30T15:45:29Z")
> [@](#): > > \*Originally posted by Kelsonk \* > This problem should be completely unimportant to me, but it’s been in the back of my mind for quite some time. > > ``` > 8/(x-3)=(x+5)/(x-3) > > ``` > > I naturally said the answer was three, but my math teacher said since (8/0) is undefined, the problem has no solution. > > (8/0)=(8/0) So it shouldn’t even matter that it’s undefined, right? Not necessarily, if you apply limits to it. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [January 30, 2003, 3:53pm UTC](https://boards.straightdope.com/t/simple-algebra-problem/151494/24 "2003-01-30T15:53:22Z")
> [@](#): > > \*Originally posted by Urban Ranger \* > \*\*Not necessarily, if you apply limits to it. \*\* Limits have nothing to do with this. It’s an algebraic equation, not a calculus problem. ---
**Author:** ![NE\_Texan](https://avatars.discourse-cdn.com/v4/letter/n/e99b99/32.png) [@NE\_Texan](https://boards.straightdope.com/u/NE_Texan)\ **Post date:** [January 30, 2003, 4:00pm UTC](https://boards.straightdope.com/t/simple-algebra-problem/151494/25 "2003-01-30T16:00:49Z")
While the original problem does not have a defined solution, you can point out that there is a unique limiting point to the solution. That is to say, if y = 8/(x-3)-(x+5)/(x-3) for all x \<\> 3, then lim[sub]y-\>0[/sub] x = 3 Which is just a mathematical way of explaining the behavior of **monica** ’s calculator graph. On preview, I see that **ultrafilter** has dismissed the idea of limits on non-calculus problems. I’ll politely disagree with him to say that limits are useful anytime you have a discontinuity in a function (which clearly is the case here), not just in calculus. ---
**Author:** ![ultrafilter](https://avatars.discourse-cdn.com/v4/letter/u/3d9bf3/32.png) [@ultrafilter](https://boards.straightdope.com/u/ultrafilter)\ **Post date:** [January 30, 2003, 4:18pm UTC](https://boards.straightdope.com/t/simple-algebra-problem/151494/26 "2003-01-30T16:18:20Z")
The question was not “what is the behavior of this function as x -\> 3?”. The question was “what are the solutions of this equation?”. Whether you use limits or not, the equation in the OP has no solution. btw, 8/(x - 3) - (x + 5)/(x - 3) = (8 - x - 5)/(x - 3) = (3 - x)/(x - 3) = -1. y doesn’t go to zero. ---
**Author:** ![RM\_Mentock](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@RM\_Mentock](https://boards.straightdope.com/u/RM_Mentock)\ **Post date:** [January 30, 2003, 4:32pm UTC](https://boards.straightdope.com/t/simple-algebra-problem/151494/27 "2003-01-30T16:32:31Z")
> [@](#): > > \*Originally posted by NE Texan \* > \*\*if y = 8/(x-3)-(x+5)/(x-3) for all x \<\> 3, then > > lim[sub]y-\>0[/sub] x = 3 > > Which is just a mathematical way of explaining the behavior of **monica** ’s calculator graph.\*\* I’m not even sure, in this instance, what you mean by the limit as y approaches zero. If you plug in values close to zero for y, what values do you get for x? They’re all undefined, so that limit doesn’t exist. Even the limit as y approaches -1 doesn’t exist. Values of y close to -1 also give undefined values for x. ---
**Author:** ![FranticMad](https://avatars.discourse-cdn.com/v4/letter/f/c68b51/32.png) [@FranticMad](https://boards.straightdope.com/u/FranticMad)\ **Post date:** [January 30, 2003, 6:16pm UTC](https://boards.straightdope.com/t/simple-algebra-problem/151494/28 "2003-01-30T18:16:11Z")
[QUOTE **FranticMad** , if you think undefined should equal undefined, then do you also think that the squareroot of an apple is equal to 8/0? \*\*[/QUOTE] I had no opinion on whether mathematics _should_ allow undefined entities to be equal. I trust mathematicians to make the right choice for purposes of internal consistency or whatever. I would love to insert the obligatory and irrelevant reference to Godel here, but maybe someone else can. I do prefer a banana to the squareroot of an apple, as one can be eaten and the other – well I don’t know what you’d do with the the root of an apple. Hence I would deem them not to be equal, but I don’t pretend that this is a mathematical answer. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [January 30, 2003, 6:25pm UTC](https://boards.straightdope.com/t/simple-algebra-problem/151494/29 "2003-01-30T18:25:55Z")
Just for an alternative viewpoint, in Matlab, with x = 3, (8/(x-3)) == ((x+5)/(x-3)) evaluates as true (although it does give divide-by-zero warnings). This is because Matlab uses the IEEE floating-point standard 754 for representing numbers, which has rules for operations involving infinities and indeterminate results (Not a Numbers). For example [from this site](http://research.microsoft.com/~hollasch/cgindex/coding/ieeefloat.html): ```auto Operation Result n / ±Infinity 0 ±Infinity x ±Infinity ±Infinity ±nonzero / 0 ±Infinity Infinity + Infinity Infinity ±0 / ±0 NaN Infinity - Infinity NaN ±Infinity / ±Infinity NaN ±Infinity x 0 NaN ``` I couldn’t find right away what the standard says about _comparisons_ involving Infinities or NaNs. I’ll keep looking. In MatLab, NaNs always compare as unequal, even with themselves. Of course, the OP was taking a math class, not a programming class, so naturally his teacher _was_ correct. BTW, If the IEEE standard 754 bothers you, know that it is currently [undergoing a revision!](http://grouper.ieee.org/groups/754/revision.html) Feel free to voice your opinions on this standard to the IEEE. As it says at the link, “Meetings are open and participation is free of charge”. 🙂 ---
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [January 30, 2003, 6:39pm UTC](https://boards.straightdope.com/t/simple-algebra-problem/151494/30 "2003-01-30T18:39:45Z")
Right, **ZenBeam** , it evaluates to true because NaN == NaN. I believe you’d get the same result if you evaluated 1/0 == 2/0. > [@](#): > > \*Originally posted by NE Texan \* > On preview, I see that **ultrafilter** has dismissed the idea of limits on non-calculus problems. I’ll politely disagree with him to say that limits are useful anytime you have a discontinuity in a function (which clearly is the case here), not just in calculus. Of course, any problem that you use limits to solve is _ipso facto_ in the realm of calculus. And your approach will give you some very unsatisfying results. For instance: What is the value of f(0) if f(x) is defined as 1 for x not equal to 0, and 0 for x = 0. The “unique limiting point to the solution” is 1, when the actual solution is clearly 0. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [January 30, 2003, 10:55pm UTC](https://boards.straightdope.com/t/simple-algebra-problem/151494/31 "2003-01-30T22:55:28Z")
> [@](#): > > Right, **ZenBeam** , it evaluates to true because NaN == NaN. I believe you’d get the same result if you evaluated 1/0 == 2/0. No, it evaluates to 8/0 == 8/0 which in turn evaluates to Inf == Inf, which is true (in Matlab, anyway). 1/0 == 2/0 also returns true in Matlab. However, NaN == NaN is always false, so for example, if x = 0/0, x == x evaluates to false. [Here’s a site](http://msdn.microsoft.com/library/default.asp?url=/library/en-us/vjref98/html/4_2_3.asp) which gives the rules for comparisons with Infs and NaNs, although I’d rather see a more authoritative source say that Inf == Inf is true under IEEE 754, and not just Microsoft’s interpretation of it. ---
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [January 30, 2003, 11:17pm UTC](https://boards.straightdope.com/t/simple-algebra-problem/151494/32 "2003-01-30T23:17:08Z")
Ah I see. I didn’t read that closely, but that makes sense too. Cool. Just out of curiosity, isn’t there such a thing as -0 in IEEE? What’s the value of n / -0? ---
**Author:** ![FranticMad](https://avatars.discourse-cdn.com/v4/letter/f/c68b51/32.png) [@FranticMad](https://boards.straightdope.com/u/FranticMad)\ **Post date:** [January 31, 2003, 3:13am UTC](https://boards.straightdope.com/t/simple-algebra-problem/151494/33 "2003-01-31T03:13:41Z")
> [@](#): > > \*Originally posted by Achernar \* > \*\*Just out of curiosity, isn’t there such a thing as -0 in IEEE? What’s the value of n / -0? \*\* I don’t suppose this would be a good time to mention square root of -1, and how it is imaginary but indispensible for correlational statistics, signal processing…no, okay, I’ll sit down. ---
**Author:** ![ZenBeam](https://avatars.discourse-cdn.com/v4/letter/z/3ab097/32.png) [@ZenBeam](https://boards.straightdope.com/u/ZenBeam)\ **Post date:** [January 31, 2003, 5:03pm UTC](https://boards.straightdope.com/t/simple-algebra-problem/151494/34 "2003-01-31T17:03:33Z")
> [@](#): > > What’s the value of n / -0? Yes, there’s a -0. n / -0 = -Inf if n \> 0, +Inf if n \< 0, NaN if n = 0 or n = NaN. ---
**Author:** ![Achernar](https://avatars.discourse-cdn.com/v4/letter/a/e274bd/32.png) [@Achernar](https://boards.straightdope.com/u/Achernar)\ **Post date:** [January 31, 2003, 6:37pm UTC](https://boards.straightdope.com/t/simple-algebra-problem/151494/35 "2003-01-31T18:37:31Z")
Okay. Then I guess 8 / 0 == 8 / -0 would probably return false, even though we think of 0 and -0 as the same. Wacky stuff… [Previous page](https://boards.straightdope.com/t/simple-algebra-problem/151494.md?page=1)