Is the expression $\frac{x^2+2x+1}{\sqrt{x}}$ a rational expression (i.e., a quotient of two polynomials)?

No — the denominator $\sqrt{x}=x^{1/2}$ is not a polynomial, so the whole expression is not a rational expression

No — because the numerator must be constant for a rational expression, and here it contains $x$ terms

Yes — because both numerator and denominator are algebraic expressions, and any algebraic quotient is a rational expression

Yes — since $x^2+2x+1$ is a polynomial and $\sqrt{x}$ can be rewritten as a polynomial for integer $x$ values only, the expression is rational for integer $x$