X-3/x-1=x-4/x-5

It's yet another real world question that's come up in conversation that I've wanted to know the answer to, and which Wolfram Alpha would be really awesome if it could handle, but sadly cannot.

anulman• 17 years ago

x = 11/3

mark-t• 17 years ago

No, x = -1/4 is correct. Perhaps you should look up the order of operations.

ars• 17 years ago

He's not all wrong. In algebraic notation division is written as a fraction, and has a lower precedence. So it's a bit ambiguous.

redcap3• 17 years ago

I'm getting x = 11/3 as well.

My workings:

(x-3)/(x-1) = (x-4)/(x-5)

(x-3)(x-5) = (x-4)(x-1)

x^2 -8x + 15 = x^2 -5x +4

-8x + 11 = -5x

11 = 3x

x = 11/3

FWIW, wolfram alpha agrees with me.

anigbrowl3• 17 years ago

In other words, bing now has some calculation abilities. MS is running an ad with this particular calculation suggested as a Bing search and a background photo of a blackboard.

Well, as you see, it works. And (I presume) they would like you think about the fact that throwing the same equation at Google does nothing useful (inexplicably, the first result was a page about BSD).

But I wonder how many users of this feature will be familiar with the rules of operator precedence? I admit I read it as:

x-3

--- = ... << I can't format it right but you get the idea

x-1

After testing it with Google, I went to Alpha, which (unsurprisingly) handled it with aplomb, giving it to me with proper notation as well and making me aware of my mistake. So I tried it as (x-3) / (x-1) = (x-4) / (x-5), which Alpha also handled with Aplomb (11/3 if you are lazy).

However, inputing the latter into Bing (without or without spaces for padding) gave no calculation or result, but just a bunch of (mostly unrelated) search results. Seems rather counter-productive on MS's part.

Apologies if this is excessively trivial.

anigbrowl3• 17 years ago

Even weirder...

(x-3)/x-1=(x-4)/x-5 works OK (ie Bing treats it as math); indeed for (x-3)/x-1=x-4/x-5 Bing properly gives both solutions 1/2(5+/-(29^0.5)).

But it absolutely Does Not Like parentheses in denominator (eg x-3/(x-1)=x-4/x-5) on either side of the equation. Clearly, I need to get out more.

forgotmypasswd• 17 years ago

google of course now links to this page first!

jerf2• 17 years ago

Please don't post homework problems to this newsgroup.

anigbrowl3• 17 years ago

Oh dear, I hope that's a joke :-/ Maybe I should have done it as a 'tell HN' type post. I thought people would be interested in the depth of the parsing tree.

jerf2• 17 years ago

Yes. I thought "newsgroup" would be a giveaway. :-/ No usenetters here, eh?

'course, people may just not like the joke.

g_• 17 years ago

I don't see the result in Bing.

alpha direct link: http://www.wolframalpha.com/input/?i=(x-3)/(x-1)%3D(x-4)/(x-...

brown9-2• 17 years ago

That's actually a different question than http://www.wolframalpha.com/input/?i=x-3%2F+x-1%3D+x-4%2F+x-...

Bing's formatting of the results doesn't quite draw your eye to it - look for "Calculation" immediately below "All Results"

michaelkeenan• 17 years ago

Are you outside the USA? I'm in Taiwan and Bing isn't calculating it for me either. It's just returning a bunch of normal search results in Chinese. Maybe calculation only works for queries coming from inside the USA.

chaosprophet• 17 years ago

Well, I'm in India and it does display the calculations for me.

zach2• 17 years ago

That's weird, I didn't see it either this afternoon, but now I do.

Pistos2• 17 years ago

FWIW: http://www.numberempire.com/equationsolver.php says -1/4. It will only give 11/3 if you explicitly put parentheses: (x-3)/(x-1)=(x-4)/(x-5) . So I believe Bing's result is correct. Based on elementary school order of operations, the implied parentheses on the original equation are: x - (3/x) - 1 = x - (4/x) - 5.

skoob• 17 years ago

For some reason, it only works for certain combinations of countries and languages. E.g., it works for Argentina: http://www.bing.com/search?q=x-3%2fx-1%3dx-4%2fx-5&setmk... but not Chile: http://www.bing.com/search?q=x-3%2fx-1%3dx-4%2fx-5&setmk...

fsniper• 17 years ago

And not for Turkey..

adatta02• 17 years ago

Live! search could do these types of calculations for sometime. It could even handle solving quadratics.

seldo• 17 years ago

Live search had an integrated exclamation point in the name?

cema• 17 years ago

An interesting, apparently unintentional, side effect is the exercise in the precedence rules.

Search engines (bing, google, wolfram) get the precedence but are finicky about calculations. Humans (presumable anyway, from the earlier comments) do the calculations but sometimes overlook the precedences. I think it is rather funny.

X-3/x-1=x-4/x-5

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