Solve 4 over x minus 4 equals the quantity of x over x minus 4, minus four thirds for x and determine if the solution is extraneous or not.
x = 4, extraneous
x = 4, non-extraneous
x = -4, extraneous
x = -4, non-extraneous

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\[\frac{4}{x-4}=\frac{x}{x-4}-\frac{4}{3}\]?

yes

there is no solution, so not sure why you are supposed to come up with one

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