Question

Solve 6 over x minus 4 equals 4 over x for x and determine if the solution is extraneous or not. Explain @SolomonZelman

Answer 1

\(\LARGE\color{blue}{ \frac{6}{x-4}=\frac{4}{x} }\) like this ?

Answer 2

Yeah

Answer 3

I would suggest

1) Cross multiply (and expand both sides)
2) subtract 4x from both sides
3) divide both sides by 2

Answer 4

You can as well:

1) Divide the numerators of both sides by 2, this will give you that the numberator on the left is 3, and numerator on the right is 2.
2) Then cross multiply.
3) subtract 2x from both sides

Answer 5

Alright now determine if the solution is extraneous or not

Answer 6

same thing in different order.

Answer 7

What solution did you get ?

Answer 8

-8

Answer 9

yup ;)

Answer 10

Thanks and later ()_()

Answer 11

Put it in, and see if it works.

\(\LARGE\color{blue}{ \frac{6}{x-4}=\frac{4}{x} }\)

\(\LARGE\color{blue}{ \frac{6}{\color{red}{-8}-4}=\frac{4}{\color{red}{-8}} }\)

\(\LARGE\color{blue}{ \frac{6}{-12}=\frac{4}{-8} }\)

\(\LARGE\color{blue}{ -\frac{1}{2}=-\frac{1}{2} }\)

Answer 12

so it works.

Answer 13

\(\Large\color{ blue }{\Large {\bbox[5pt, lightcyan ,border:2px solid white ]{ \rm{Anytime!}\Huge{^✍} }}}\)