Question

Solve 6 over x minus 3 equals 3 over x for x and determine if the solution is extraneous or not

Answer 1

\[\frac{ 6 }{ x }-3=\frac{ 3 }{ x }\]

Answer 2

Do you see how I got this equation?

Answer 3

Since it is the same denominator, we can solve for like terms.
\[\frac{ 6 }{ x }-3=\frac{ 3 }{ x }\]
\[\frac{ 6 }{ x }-\frac{ 6 }{ x }-3=\frac{ 3 }{ x }-\frac{ 6 }{ x }\]

Answer 4

Correct?
Sorry for being slow, the equation was hard to type

Answer 5

the answer was x=-3, but I don't know how to do the extraneous part

Answer 6

\[3=-\frac{ 3 }{ x }\]

\[3 \times x=-\frac{ 3 }{ x }\times x\]

\[3x=-3\]

\[x=-1\]

Answer 7

x was negative one. Do you see your mistake?

Answer 8

that's not an option

Answer 9

Wait really lol

Answer 10

My apologies

Answer 11

x would be positive one. I forgot to carry the negative.

Answer 12

Is that an option?

Answer 13

That makes sense.
I thought the minus three was not apart of the fraction. Let me redo it.

Answer 14

For step one, you can get rid of the denominator for the products side.
Step two, getting rid of the denominator for the left hand side.
Agree?

Answer 15

6x=3x-9
-3x -3x

3x=-9

x=-3

Answer 16

And to figure out if the solution is extraneous, we will plug it in the equation given.

Answer 17

So your answer is D.

Answer 18

yeah that's what I got lol

Answer 19

okay thankyou somuch

Answer 20

You're welcome!