RationalExpressionQ

RationalExpressionQ[expr,x] gives True if expr is structurally a rational expression in x, and False otherwise.

RationalExpressionQ[expr,{x,y,…}] gives True if expr is structurally a rational expression in x,y,…, and False otherwise.

RationalExpressionQ[expr,{x,y,…},test] gives True if expr is structurally a rational expression in x,y,… with coefficients satisfying test, and False otherwise.

Examples

Test if an expression is rational in x:

RationalExpressionQ[(x^2 + 1)/(x - 1), x]
(* True *)

RationalExpressionQ[Sin[x]/x, x]
(* False *)

Please visit the official Wolfram Language Reference for more details.