`|frac{2x}{3} - 2| = |frac{x}{3} + 3|`

`x^4-: (x^4 - 1)`

One
student told me every time he talks to a tutor he gets a different
way to get
common denominators and, truthfully, he was confused by
all the explanations.
How would you explain this problem to a student
in this situation? The problem
is:

Simplify:

`1/(x - 3) + 2/(3 - x)`

1) Calculate the volume (V) for `1 le x lt oo` and show

that it is finite.
(hint. `V = int_1^oo pi y^2 dx`)

2) Calculate the
surface area (S) for `1 le x lt oo` and/or
show that it diverges.
(hint. `S =
int_1^oo 2 pi y sqrt(1+(dy/dx)^2)dx`)

3) It seems that you can paint the
entire surface (S)
by pouring a finite amount of paint (V) into the horn,

even though S is infinite. What do you think?