Answer
The $x$-intercept: $(-4,0)$.
Work Step by Step
(a) Using a graphing utility, the graph of the function is as shown. The $x$-intercept shown is $(-4,0)$.
(b) Setting $y=0$:
$$0=\frac{1}{x+5}+\frac{4}{x}$$ $$0=\frac{x+4(x+5)}{x(x+5)}$$ $$0=x+4x+20$$ $$0=5x+20$$ $$-5x=20$$ $$x=\frac{20}{-5}$$ $$x=-4$$
Thus, result in part (a) is confirmed.
