Question

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

Answer 1

Answer:

c

Step-by-step explanation:

Answer 2

$\frac{4}{x-4} = \frac{x}{x-4}- \frac{4}{3}$
$\frac{4}{x-4}- \frac{x}{x-4} =- \frac{4}{3}$
$\frac{4-x}{x-4}=- \frac{4}{3}$
$3(4-x)=-4(x-4)$
$12-3x=-4x+16$
$4x-3x=16-12$
$x=4$

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

$\frac{4}{4-4}= \frac{x}{4-4}- \frac{4}{3}$
$\frac{4}{0}= \frac{x}{0}- \frac{4}{3}$

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

Correct answer: A