Problem #8: Consider the following function.
$f(x) = \sqrt{x - 1} + \frac{1}{(x - 1)^7}$
Find functions $h(x)$ and $g(x)$ such that $f = g \cdot h$.
(A) $h(x) = x + 1$, $g(x) = \sqrt{x + 1} - \frac{1}{(x + 1)^7}$ (B) $h(x) = x - 1$, $g(x) = \sqrt{x - 1} + \frac{1}{(x - 1)^7}$
(C) $h(x) = \sqrt{x - 1}$, $g(x) = \frac{1}{(x - 1)^7}$ (D) $h(x) = x - 1$, $g(x) = \sqrt{x} + \frac{1}{x^7}$
(E) $h(x) = \sqrt{x} + \frac{1}{x^7}$, $g(x) = x - 1$ (F) $h(x) = x + 1$, $g(x) = \sqrt{x} - \frac{1}{x^7}$
(G) $h(x) = \sqrt{x - 1} + \frac{1}{(x - 1)^7}$, $g(x) = x - 1$ (H) $h(x) = \sqrt{x} - \frac{1}{x^7}$, $g(x) = x + 1$