Reading the result
Rational mode analyses numerator and denominator polynomials. Custom mode also accepts arithmetic rational expressions, including negative integer powers; those receive the same polynomial analysis. Other supported scientific expressions, such as sin(x), tan(x), log(x) and sqrt(x), receive a clearly labelled numerical screen over the selected interval, in radians. Finite sampling cannot prove all asymptotes, one-sided limits or end behaviour. A blank candidate list in numerical mode does not prove absence.
Why your number may differ
The reference returns x = NaN for the default denominator x − 1. Its root is x = 1. The quotient is x + 1 with remainder −3, so the slant asymptote is y = x + 1. Cancellation distinguishes removable holes from poles; a shared root can remain a pole when its denominator multiplicity is greater. Horizontal asymptotes can be crossed. Root finding and plots use numerical tolerances, not symbolic proof for ill-conditioned high-degree input. See OpenStax on limits.