Question

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

x = -8, extraneous

x = -8, non-extraneous

x = 8, extraneous

x = 8, non-extraneous

Answer 1

6 over x minus 4 equals 4 over x x
\[\Large \frac {6}{x-4} = \frac {4}{x^2}\] is this your equation...? @ajl96 ?

Answer 2

\[\Large \frac {6}{x-4} = \frac {4}{x^2} \] --> cross multiply
\[\Large \frac {6}{x-4} = \frac {4}{x^2} \] becomes--->
\[\Large {6}({x^2}) = {4}({x-4}) \]

Answer 3

\[\Large {6}({x^2}) = {4}({x-4}) \] --> rearrange to form quadratic
\[\Large 6x^2 = 4x-16 \]
\[\Large 6x^2 - 4x+16 = 0 \] --> use quadratic formula to solve from here