Question

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. (1 point)

Answer 1

x=4, extraneous

Explanation:

Just took (05.08) test

Answer 2

I'm thinking this is what the problem looks like:
`(4)/(x-4)= (x)/(x-4)- (4)/(3)`. The first thing to do is to move the
`(x)/(x-4)` over to the other side because it has a common denominator with the other side. Doing that and at the same time combining them over their common denominator looks like this:
`(4-x)/(x-4)= -(4)/(3)`. The best way to solve for x now is to cross-multiply to get 3(4-x)=-4(x-4). Distributing through the parenthesis is 12 - 3x = -4x + 16. Solving for x gives us x = 4. Of course when we sub a 4 back in for x we get real problems, don't we? Dividing by zero breaks every rule in math that there ever was! So, yes, the solution is extraneous.