Chapter 4 - 4.2 - Graphs of Rational Functions - 4.2 Exercises - Page 324: 74

(a) The graph of the rational function intercepts the x-axis when $x=-2$ and $x=1$. The x-intercepts are: $(-2,0)$ and $(1,0)$ (b) Algebraically $y=0$ when $x=-2$ and when $x=1$ The x-intercepts are: $(-2,0)$ and $(1,0)$

$y=x-\frac{2}{x+1}$ $0=x-\frac{2}{x+1}$ $x=\frac{2}{x+1}$ $x^2+x=2$ $x^2+x-2=0$ $x^2+2x-x-2=0$ $x(x+2)-1(x+2)=0$ $(x-1)(x+2)=0$ $x-1=0$ $x=1$ $x+2=0$ $x=-2$