## anonymous one year ago is x=6 extranous or no

1. anonymous

@taramgrant0543664

2. xapproachesinfinity

where is the equation?

3. xapproachesinfinity

you want me to make one lol

4. anonymous

5. xapproachesinfinity

ok good!! what did you do thus far?

6. anonymous

igt x=6

7. anonymous

but ineed to know if its extranous or not

8. xapproachesinfinity

well put it back into the equation and see if it does work? if we put six what is the problem?

9. xapproachesinfinity

It does not really work does it?

10. xapproachesinfinity

that will produce division by zero yes? which is not allowed

11. xapproachesinfinity

you agree or disagree? what is your stance?

12. xapproachesinfinity

hhhh well can we divide by 0 can we have 6/0 in the left in the right 6/0-6/2

13. xapproachesinfinity

what is 6/0? can you have an answer?

14. anonymous

not so not extanrous

15. xapproachesinfinity

ok once step at a time what is extraneous solution

16. 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

17. 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.

18. xapproachesinfinity

yeah that's the definition right there so from the start x=6 is excluded from domain yes

19. xapproachesinfinity

but when you were solving the equation to transform it using some maneuvers then you got x=6

20. xapproachesinfinity

that's why we say it is extraneous solution because it is not included in the domain

21. 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

22. xapproachesinfinity

slight mistake first should be 6/x-6

23. xapproachesinfinity

so $\frac{6}{x-6}=\frac{x}{x-6}-\frac{6}{2}$ $\frac{6}{x-6}=\frac{2x-6}{2(x-6)}$ $\frac{6}{\cancel {x-6}}=\frac{2x-6}{2\cancel{(x-6)}}$ $6=\frac{2x-6}{2}\Longrightarrow 12 =2x-6 \Longrightarrow x=9$

24. xapproachesinfinity

how did you got x=6?

25. xapproachesinfinity

i got 9

26. xapproachesinfinity

oh my bad i miss something

27. xapproachesinfinity

correct the solution found is x=6 just missed up above in line 2

28. xapproachesinfinity

so 6 we said excluded therefore it is extraneous

29. xapproachesinfinity