Asymptote Calculator and Rational Function Grapher

Enter a polynomial on top and a polynomial underneath and this finds the asymptotes of the fraction. It cancels any common factor exactly first, which is what separates a hole in the graph from a vertical asymptote, then reads the vertical asymptotes off the remaining denominator, compares degrees for a horizontal one, and divides top by bottom for a slant one. You also get the domain, the intercepts, which way the curve runs at each pole, and a sketch with the asymptotes drawn in. It reads polynomials in x up to degree six, with brackets and products; trigonometric, exponential, logarithmic and radical functions are outside it.

One variable, called x. Brackets and products are fine: (x - 2)(x + 3). Degree 6 at the most.
Leave it as 1 for a polynomial, which has no asymptotes at all.
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