Question

Solve 4/x-4=x/x-4-4/3 for x and determined if the solution is extraneous or not.

A. X=4, extraneous
B.x=4,non-extraneous
C. X= -4, extraneous
D. X= -4, non extraneous

Answer 1

c

Explanation:

Answer 2

`(4)/(x-4) = (x)/(x-4)- (4)/(3)`

`(4)/(x-4)- (x)/(x-4) =- (4)/(3)`

`(4-x)/(x-4)=- (4)/(3)`

`3(4-x)=-4(x-4)`

`12-3x=-4x+16`

`4x-3x=16-12`

`x=4`

The solution is extraneous one because although it is a result of solving algebraically, it is not a valid solution. If we substitute x = 4 back into the equation, we will have two fractions with denominator of zero


`(4)/(4-4)= (x)/(4-4)- (4)/(3)`

`(4)/(0)= (x)/(0)- (4)/(3)`

A fraction with zero denominators is undefined, hence the solution is not valid.

Correct answer: A