Answer
The $x$-intercepts: $(-2,0)$ and $(3,0)$
Work Step by Step
(a) Using a graphing utility, the graph of the function is as shown. The $x$-intercepts shown are $(-2,0)$ and $(3,0)$.
(b) Setting $y=0$:
$$0=x-\frac{6}{x-1}$$ $$0=\frac{x(x-1)-6}{x-1}$$ $$0=x^2-x-6$$ $$0=(x+2)(x-3)$$ $$x+2=0$$ $$x=-2$$ $$x-3=0$$ $$x=3$$
Thus, the resulting equation is $x=-2$ and $x=3$, and the result in part (a) is confirmed.
