List the following functions from smallest to largest.
$$\frac{x^2 + 2}{x-1},\frac{x^2 - 2}{x+1},\frac{x + 1}{x^2-2},\frac{x + 2}{x^2-1}$$
To solve the problem, I believe we compare each fraction with each other. In order to figure out if a number is bigger than another number, we can subtract the numbers from each other, and see if they are bigger than zero (positive, negative). For example:
$$If A < B \enspace , \enspace 0 < B - A.$$
The same thing is applied to the polynomials, for instance:
$$\frac{x^2 + 2}{x-1} - \frac{x^2 - 2}{x+1} = \frac{2x^2 + 4x}{(x-1)(x+1)} > 0$$
Because the leading coefficient is the same sign, the value is always positive, therefore $$\frac{x^2 + 2}{x-1} > \frac{x^2 - 2}{x+1}$$
Am I on the right track here?