Answer
(a) The graph is as shown.
(b) The $x$-intercept is $(-1,0)$.
(c) The solution is: $x=-1$
(d) The result in part (c) is the same with the $x$-intercept of the graph.
Work Step by Step
(a) The graph is as shown.
(b) The $x$-intercept is $(-1,0)$.
(c) Setting $y=0$:
$$0=\frac{1}{x}-\frac{4}{x-1}-1$$
$$0=\frac{x-1-4x-x(x-1)}{x(x-1)}$$
$$0=-3x-1-x^2+x$$
$$0=-x^2-2x-1$$
$$x^2+2x+1=0$$
$$(x+1)^2=0$$
$$x+1=0$$
$$x=-1$$
Thus, the solution is:
$$x=-1$$
(d) The result in part (c) is the same with the $x$-intercept of the graph.
