anonymous
  • anonymous
is x=6 extranous or no
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
xapproachesinfinity
  • xapproachesinfinity
where is the equation?
xapproachesinfinity
  • xapproachesinfinity
you want me to make one lol

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anonymous
  • anonymous
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xapproachesinfinity
  • xapproachesinfinity
ok good!! what did you do thus far?
anonymous
  • anonymous
igt x=6
anonymous
  • anonymous
but ineed to know if its extranous or not
xapproachesinfinity
  • xapproachesinfinity
well put it back into the equation and see if it does work? if we put six what is the problem?
xapproachesinfinity
  • xapproachesinfinity
It does not really work does it?
xapproachesinfinity
  • xapproachesinfinity
that will produce division by zero yes? which is not allowed
xapproachesinfinity
  • xapproachesinfinity
you agree or disagree? what is your stance?
xapproachesinfinity
  • xapproachesinfinity
hhhh well can we divide by 0 can we have 6/0 in the left in the right 6/0-6/2
xapproachesinfinity
  • xapproachesinfinity
what is 6/0? can you have an answer?
anonymous
  • anonymous
not so not extanrous
xapproachesinfinity
  • xapproachesinfinity
ok once step at a time what is extraneous solution
xapproachesinfinity
  • xapproachesinfinity
let me answer this, it is a solution that you find by correct algebraic maneuvers but it does not work for the equation when we put it back
anonymous
  • anonymous
An extraneous solution is a root of a transformed equation that is not a root of the original equation because it was excluded from the domain of the original equation.
xapproachesinfinity
  • xapproachesinfinity
yeah that's the definition right there so from the start x=6 is excluded from domain yes
xapproachesinfinity
  • xapproachesinfinity
but when you were solving the equation to transform it using some maneuvers then you got x=6
xapproachesinfinity
  • xapproachesinfinity
that's why we say it is extraneous solution because it is not included in the domain
xapproachesinfinity
  • xapproachesinfinity
here is what we do \[\frac{x}{x-6}=\frac{x}{x-6}-\frac{6}{2}\] domain here is every real number except 6
xapproachesinfinity
  • xapproachesinfinity
slight mistake first should be 6/x-6
xapproachesinfinity
  • xapproachesinfinity
so \[\frac{6}{x-6}=\frac{x}{x-6}-\frac{6}{2}\] \[\frac{6}{x-6}=\frac{2x-6}{2(x-6)}\] \[\frac{6}{\cancel {x-6}}=\frac{2x-6}{2\cancel{(x-6)}}\] \[6=\frac{2x-6}{2}\Longrightarrow 12 =2x-6 \Longrightarrow x=9\]
xapproachesinfinity
  • xapproachesinfinity
how did you got x=6?
xapproachesinfinity
  • xapproachesinfinity
i got 9
xapproachesinfinity
  • xapproachesinfinity
oh my bad i miss something
xapproachesinfinity
  • xapproachesinfinity
correct the solution found is x=6 just missed up above in line 2
xapproachesinfinity
  • xapproachesinfinity
so 6 we said excluded therefore it is extraneous
xapproachesinfinity
  • xapproachesinfinity
was that helpful? clear?

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