[Maxima-bugs] [ maxima-Bugs-1303241 ] solve ((2*x)/(x+5)=1/(x^2+3*x-10),x); gives wrong answer

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Bugs item #1303241, was opened at 2005-09-24 08:39
Message generated for change (Comment added) made by robert_dodier
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Category: None
Group: None
>Status: Closed
Resolution: Invalid
Priority: 5
Submitted By: Benjamin Lau (blwy10v)
Assigned to: Nobody/Anonymous (nobody)
Summary: solve ((2*x)/(x+5)=1/(x^2+3*x-10),x); gives wrong answer

Initial Comment:
When I keyed in "solve ((2*x)/(x+5)=1/(x^2+3*x-10),x);"
Maxima reports the answers as:

x = - ( ( sqrt ( 6 ) - 2 ) / 2 )
x = ( sqrt ( 6 ) + 2 ) / 2

Where in fact, there is an additional root x = -5

I'm using the latest version of Maxima, Maxima 5.9.1 on
a Windows XP SP2 Home Edition.

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>Comment By: Robert Dodier (robert_dodier)
Date: 2006-03-25 18:48

Message:
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Closing this report since it is already marked "invalid" and
the most recent comment says the same thing.

I will open a separate report about simplification x^2/x -->
x . (I can't find an existing report about that.)

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Comment By: Stavros Macrakis (macrakis)
Date: 2005-09-28 08:12

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x=-5 is not a root of your original equation, since your
original equation is undefined at x=-5.

This is similar to the equation 1/x=2/x, which has no roots,
although cross-multiplication gives 2*x=1*x, with solution x=0.

About van Nek's example, Maxima simplifies x^2/x to x
without noting that the simplification assumes that x <> 0.
 This is a known issue, but unfortunately not easy to deal
with -- how would we keep track of the context in which x<>0?

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Comment By: Volker van Nek (van_nek)
Date: 2005-09-24 12:15

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Hello,
in this case solve gives the correct answer.
Your expression is not defined for x = -5.

Problematic is the following 
(%i5) eq: (x-1)^2/(x-1)=0$
(%i6) solve(eq,x);
(%o6) 				    [x = 1]

My expression is not defined for x = 1.
I get a solution, where there should not be a solution.

Volker van Nek


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Comment By: Benjamin Lau (blwy10v)
Date: 2005-09-24 09:07

Message:
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user_id=1128112

Maxima version: 5.9.1
Maxima build date: 7:34 9/24/2004
host type: i686-pc-mingw32
lisp-implementation-type: Kyoto Common Lisp
lisp-implementation-version: GCL 2.6.5

The above is the information that I just realised need to be
added.

Benjamin Lau [the original bug postee of this]

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