## anonymous one year ago Classify the solutions of 1 over x plus 4, plus one half, equals 1 over x plus 4 as extraneous or non-extraneous

1. misty1212

lol there is either a solution, or there is not not sur what math teacher made up this "extraneous' nonsense

2. misty1212

$\frac{1}{x+4}+\frac{1}{2}=\frac{1}{x+4}$? is that the question?

3. anonymous

i just need help with the extraneous and non extraneous

4. anonymous

yes that is

5. misty1212

6. misty1212

oh ok then lets think

7. misty1212

x is a variable, it can be anything but whatever it is on the left, it is the same on the right so if you add one half to a number, it is impossible to get the same number back there is NO SOLUTION

8. anonymous

the answer is x= -4 but idk if its extraneous or not

9. misty1212

THE ANSWER IS NOT X = -4

10. anonymous

then what is it? bc i followed the directions in the lesson

11. misty1212

ok fine, say $$x=-4$$ is "extraneous" if that will make your math teacher happy

12. anonymous

do you know the difference between the two?

13. misty1212

$\overbrace{\frac{1}{x+4}}^{\text{this}}+\frac{1}{2}=\overbrace{\frac{1}{x+4}}^{\text{is equal to this}}$

14. anonymous

ok

15. misty1212

you cannot add one half to a number and get the same number back

16. misty1212

the not very bright math teacher who wants you not to think like a person, but do some steps to "solve" wants you to find that $$x=-4$$ but $$x$$ cannot be $$-4$$ because a) that would make the denominator zero and b) there is NO SOLUTION

17. misty1212

therefore they want you to behave like a robot and say "the solution is $$x=-4$$ but it is "extraneous""

18. anonymous

x = −4; extraneous x = −4; non-extraneous x = −8; extraneous x = −8; non-extraneous so out of these answer choices......its the first one?

19. anonymous

@misty1212