Question

Solve 6/x-4 = 4/x and determine if the solution is extraneous or not. Medal given! please help!

Answer 1

@zepdrix @campbell_st

Answer 2

\[\Large\bf\sf \frac{6}{x-4}\quad=\quad \frac{4}{x}\]Is this the problem?

Answer 3

yes

Answer 4

So ummm how should we approach this...
Remember how to cross multiply?

Answer 5

yes

Answer 6

would it be... 6x = (x-4)(4)

Answer 7

mmm ok good

Answer 8

So we need to distribute the 4 to each term in the brackets, yes?

Answer 9

yea

Answer 10

(4)(x-4) = 4x-16

Answer 11

the choices are:

Answer 12

woops what happened in the middle there...

6x-4x= 16
2x = 16, right?

Answer 13

x= -8, extraneous
x= -8, non-extraneous
x= 8, extraneous
x= 8, non- extraneous

Answer 14

woops, its 8

Answer 15

typo

Answer 16

Extraneous means BAD!
If we plug 8 back into the original problem, does it cause a problem?
Does it cause us to divide by zero in any spot?

Answer 17

nope

Answer 18

so non-extraneous

Answer 19

Yay good job!

Answer 20

ugh that was easy.. I could've done that one myself... could you help me with a harder one like that

Answer 21

Oooo we made a little boo boo hold on!

Answer 22

oh no where

Answer 23

\[\Large\bf\sf 6x\quad=\quad 4x-16\]Subtracting 4x to each side should have given you,\[\Large\bf\sf 6x-4x\quad=\quad -16\]\[\Large\bf\sf 2x\quad=\quad -16\]

Answer 24

ohh

Answer 25

so -8

Answer 26

non-extraneous

Answer 27

mm k ya i think we've got it now! c:

Answer 28

ok here's my last one

Answer 29

can u help me quickly, i need to do something in a few minutes before i leave the house :/

Answer 30

\[\Large\bf\sf \frac{6}{x-6}\quad=\quad \frac{x}{x-6}-\frac{6}{2}\]There's a few different ways to do this one.
See how we have a couple fractions with the same denominator?
Let's combine those by getting them on the same side.
So we'll subtract x/(x-6) from each side.\[\Large\bf\sf \frac{6}{x-6}-\frac{x}{x-6}\quad=\quad -\frac{6}{2}\]
\[\Large\bf\sf \frac{6-x}{x-6}\quad=\quad -\frac{6}{2}\]

Answer 31

Then from there you can cross multiply again I guess.

Answer 32

wait! stay here

Answer 33

(2)(6-x)= (-6)(x-6)

Answer 34

12-2x = -6x+36

Answer 35

k looks good so far!

Answer 36

-2x+6x= -12+36

Answer 37

-4x= 24
x= -6

Answer 38

do you think its extraneous or non?

Answer 39

\[\Large\bf\sf -2x+6x\quad\ne\quad -4x\]

Answer 40

huh?

Answer 41

oh

Answer 42

4x?

Answer 43

ya

Answer 44

ok

Answer 45

4x= 24
x= 6

Answer 46

so is it extraneous or non-extraneous

Answer 47

Hmm does it cause any problems when we try to plug it back into the original?\[\Large\bf\sf \frac{6}{\color{red}{6}-6}\quad=\quad \frac{\color{red}{6}}{\color{red}{6}-6}-\frac{6}{2}\]

Answer 48

yea

Answer 49

Hmm ya, looks like it's giving us zeros in our denominators.
Bad! Extraneous! :O

Answer 50

thanks so much! i gtg now! :)

Answer 51

bb \c: