Rational function and domain for JEE

Formula

\[r(x)=\frac{p(x)}{q(x)},\qquad D(r)=\{x:q(x)\neq 0\}\]

Variables: \(p,q\) are polynomials.

Conditions: Exclude zeros of denominator.

Domain, continuity, discontinuity, asymptotes, differentiability.