Answer
The $x$-intercept: $(-3,0)$
Work Step by Step
(a) Using a graphing utility, the graph of the function is as shown. The $x$-intercept shown is $(-3,0)$.
(b) Setting $y=0$:
$$0=20\left(\frac{2}{x+1}-\frac{3}{x}\right)$$ $$0=\frac{2}{x+1}-\frac{3}{x}$$ $$0=\frac{2x-3(x+1)}{x(x+1)}$$ $$0=2x-3x-3$$ $$0=-x-3$$ $$x=-3$$
Thus, result in part (a) is confirmed.
