EXPLANATION :
From the problem, we have :
[tex]\frac{x}{x-4}=\frac{4}{x-4}[/tex]
Using cross multiplication :
[tex]\begin{gathered} x(x-4)=4(x-4) \\ x^2-4x=4x-16 \\ x^2-4x-4x+16=0 \\ x^2-8x+16=0 \\ \text{ Factor completely :} \\ (x-4)(x-4)=0 \\ \text{ Equate factors to 0} \\ x-4=0 \\ x=4 \end{gathered}[/tex]
The value of x is 4
But this value of x will make the expression or equation undefined.
Because the denominator will become 0.
[tex]\begin{gathered} \frac{x}{x-4}=\frac{4}{x-4} \\ \\ \frac{4}{4-4}=\frac{4}{4-4} \\ \\ \frac{4}{0}=\frac{4}{0} \end{gathered}[/tex]
Therefore, the result of x = 4 is NOT valid.
