Rational Expressions

1. You can assign a rational expression to a variable:
> r := 1/(x+1) -1/(x-1);

                                 1       1
                          r := ----- - -----
                               x + 1   x - 1

2. You can simplify this expression:
> simplify(r);

                                   2
                          - ---------------
                            (x + 1) (x - 1)

> denom(simplify(r));

                           (x + 1) (x - 1)

> numer(simplify(r));

                                  -2

> plot(r, x=-10..10);

3. You can force Maple to plot just the points
that it computes for a graph of an expression:
> plot(r, x=-10..10, style=POINT);

> solve(denom(r));

                                -1, 1

> plot(r, x=-2..2,y=-30..30, style=POINT);

> s := (x^2 +5*x +6)/(x^3 +2*x^2 -x -2);

                                2
                               x  + 5 x + 6
                        s := -----------------
                              3      2
                             x  + 2 x  - x - 2

> factor(numer(s));

                           (x + 3) (x + 2)

> factor(denom(s));

                       (x - 1) (x + 2) (x + 1)

> simplify(s);

                                x + 3
                                ------
                                 2
                                x  - 1

> plot(s,x=-3..3, y=-30..30);

>