Chapter 11 - Rational Expressions and Functions - 11-4 Adding and Subtracting Rational Expressions - Practice and Problem-Solving Exercises - Page 677: 47

$\frac{-3x-5}{x(x-5)}$

We are given that $f(x) = 8x, g(x) = \frac{1}{x}, and h(x) = \frac{4}{x-5}$ to solve this problem. Therefore, $g(x) - h(x) = \frac{1}{x} - \frac{4}{x-5} =\frac{1(x-5)}{x(x-5)} - \frac{4x}{x(x-5)} = \frac{(x-5)-4x}{x(x-5)} =\frac{x-5-4x}{x(x-5)} = \frac{x-4x - 5}{x(x-5)} =\frac{-3x-5}{x(x-5)} $