Answer
$x = 6$
Work Step by Step
1. Multiply by $x-5$ on both sides of the equation to obtain:
$\frac{x}{x-5} - 4 = \frac{2}{x-5}$
$x - 4(x-5) = \frac{2(x-5)}{x-5}$
2. Cancel out $x-5$ in the fraction to simplify:
$x -4(x-5) = 2$
3. Expand and solve for $x$:
$x - 4x + 20 = 2$
$-3x + 20 -2 = 0$
$-3x + 18 = 0$
$-3(x - 6) = 0$
$x-6 = 0$
$x = 6$
