#### Answer

The equation has no solution.

#### Work Step by Step

$\dfrac{x}{x-4}=\dfrac{4}{x-4}+4$
Multiply the whole equation by $x-4$:
$(x-4)\Big(\dfrac{x}{x-4}=\dfrac{4}{x-4}+4\Big)$
$x=4+4(x-4)$
Evaluate the indicated operations:
$x=4+4x-16$
Take $4x$ to the left side:
$x-4x=4-16$
Simplify both sides:
$-3x=-12$
Solve for $x$:
$x=\dfrac{-12}{-3}$
$x=4$
The original equation is undefined for $x=4$, so the equation has no solution.