Answer
(a) The graph is as shown.
(b) The $x$-intercept is $(2,0)$.
(c) The solution is: $x=2$
(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 $(2,0)$.
(c) Setting $y=0$:
$$0=x+\frac{9}{x+1}-5$$
$$0=\frac{x(x+1)+9-5(x+1)}{x+1}$$
$$0=\frac{x^2+x+9-5x-5}{x+1}$$
$$0=x^2-4x+4$$
$$(x-2)^2=0$$
$$x-2=0$$
$$x=2$$
Thus, the solution is:
$$x=2$$
(d) The result in part (c) is the same with the $x$-intercept of the graph.
