The following expressions in examples aren't polynomial expressions:
$2x^2-5x+(3/x)$ $9- \sqrt x$
Neither they are rational expressions, I've been just told that by book. but then what do you call them?
The following expressions in examples aren't polynomial expressions:
$2x^2-5x+(3/x)$ $9- \sqrt x$
Neither they are rational expressions, I've been just told that by book. but then what do you call them?
The two examples you gave are both algebraic functions, i.e. functions that satisfy a polynomial equation whose coefficients are rational functions. For example, $f=9-\sqrt{x}$ satisfies the polynomial equation $(y-9)^2-x=y^2-18y+(81-x)=0,$ i.e. $y=f$ is a root of this polynomial, and the coefficients of the polynomial are the rational functions $1$, $-18$, and $81-x$. However, as has been pointed out in the comments, $g=2x^2-5x+\tfrac{3}{x}$ is itself a rational function, so there is a particularly simple polynomial it satisfies (specifically, a linear polynomial) $y-(2x^2-5x+\tfrac{3}{x})=0.$
I suppose you could call them Puiseux polynomials by analogy with Puiseux series, though I'm not sure anyone has ever done so.